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As they embark on their Princeton University careers, 15 freshmen are grappling with a question that will be central to their lives: What is the meaning of a good life?
The question is just one of many raised in the freshman seminar "Individuality as an Ideal," which is being taught this fall by Kwame Anthony Appiah, the Laurance S. Rockefeller University Professor of Philosophy and the University Center for Human Values. Appiah is a world-renowned moral and political philosopher who has taught at Princeton since 2002.
"Individuality is a great example of a topic that is both intellectually challenging and profoundly relevant to thinking about how one lives one's own life," Appiah said.
He added, "It's a perfect introduction to a liberal education ... which is an education that prepares you for a life as a free individual, in charge of interpreting your situation and marshaling the resources that you've gotten from your genome, your family, your school, your society, to manage the one life you have."
Ankit Buddhiraju said he was drawn to the seminar because he wanted to discuss how individuality might be defined, and how it "has been associated with a gamut of personal qualities, both positive and negative, such as creativity, originality, nonconformity and selfishness."
For Gabriella Ravida, the class is allowing her to do something new. "I chose the seminar because I never took any philosophy classes in high school, and I wanted to start my college experience on a new note," she said.
To engage with such a thought-provoking subject, the course, which is designated as the Kurt and Beatrice Gutman Freshman Seminar in Human Values, encourages broad-ranging conversations that stem from readings of novels and philosophy.
Each class starts with a presentation by a student who summarizes and analyzes that week's texts, after which the group is invited to offer further comments.
On a recent evening, the discussion centered on Aristotle's notion of ethics and his concept of eudaemonia, which is the idea of a life well lived.
"This is hard stuff," cautioned Appiah, before asking the evening's presenter, Andrew Barnett, and the class to "go bravely into it." He encouraged the freshmen to "keep an eye on the big picture" as they gained a general sense of the ancient Greek philosopher's intellectual approach.
In his presentation, Barnett emphasized Aristotle's belief that "you need ethics in order to live the best life," and that "without a central good in life, all other things lose meaning." He also stressed the importance of self-examination and the utilitarian understanding that to live well, one must also take action for the good of others.
The discussion expanded to the students seated around the long table, as they explored a variety of terms — happiness, pleasure, excellence, virtue, morality — with Appiah providing guiding principles and examples.
The conversation drew from texts covered earlier in the class, in particular the 19th-century philosopher and political economist John Stuart Mill's third chapter of his essay "On Liberty," called "Individuality as One of the Elements of Wellbeing."
The students also could think back on the novels they had read from different countries and time periods, whose main characters struggle to shape their lives in the face of changing societal landscapes. The readings included Chinua Achebe's "Things Fall Apart," Tsitsi Dangarembga's "Nervous Conditions," Stendhal's "The Red and the Black," and Kazuo Ishiguro's "The Remains of the Day."
Later in the semester, the students will explore philosophical works by Ralph Waldo Emerson, Ronald Dworkin, Michel Foucault, Friedrich Nietzsche and Joseph Raz, as well as the literary critic Lionel Trilling.
Freshman Bina Peltz said the variety of the readings, along with the varied backgrounds of the students, provides a fertile environment for new ideas. "The diverse experiences of the other students engender a unique fusion of interpretations," she said, "while Professor Appiah's vast knowledge constantly offers us a fresh perspective."
To evoke new perspectives, Appiah asked the students if they could offer two examples of ways of living that were worth pursuing, but that were very different from each other.
One student said, "Traveling the world and experiencing different cultures, or building a stable home and raising a family."
Delighted with the juxtaposition, Appiah offered a famous example: the life of the French post-impressionist artist Paul Gauguin, who abandoned his wife and children in order to move to Tahiti, a setting that inspired his work and propelled him to fame.
Appiah elaborated that the 20th-century British philosopher Bernard Williams used the example of Gauguin to ask the central question about which of the choices available to the artist pointed to a better life.
Going to Tahiti, said Appiah, "paid off," even at the cost of Gauguin's family. "If the life in Tahiti had amounted to nothing, we would have had a negative assessment of his life," he said. "What he did was morally wrong," but by making the choice that enabled his artistry to flourish, Gauguin ended up with a "great life, with flaws in it, but that's less important."
The example of greatness spurred a fresh question from a student who asked if more should be said about the life worth living of a "regular person."
Returning to Aristotle, Appiah answered that while the teachings of the ancient philosopher at that time addressed the well educated and the aristocracy — including Alexander the Great, who was tutored by Aristotle — he did provide numerous examples of elements that were, and remain, important to everybody for a life worth living.
"Friendships, being moral, being a decent person, not causing unnecessary harm to others, that's there for everybody," Appiah said.
Appropriate for students new to college and to Princeton, questions also surfaced about using the resources one has to advance oneself, as well as the role of ambition in building a life worth living.
"Aristotle teaches us that high ambitions not achieved might be a great life, but low ambitions achieved may not be such a good life," Appiah said.
He reminded the students, though, that Mill "makes it very clear that there are different strokes for different folks," and that "people have the right to do what they do because that is up to them."
It's a message that Appiah takes to heart himself. He wants to encourage these new Princeton students to reach high to achieve intellectual and personal goals, but he in no way wants to tell them what to do.
"It's my job to help them deepen their grasp of how to manage their lives for themselves," Appiah said. "And each time I teach about this topic, I learn new things from them as I hope they learn new things from me. It's a great privilege to have these amazing young people in class."


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Northwestern University, the 20th-ranked college football team in the nation, won't win a national title on the field this year. But the Wildcats are first in the classroom, according to the "Academic BCS," the New America Foundation's annual academic performance rankings of the top-25 college football teams.
Northwestern's top finish is not surprising. But the New America Foundation's second-best academic team, Northern Illinois — which finished ahead of schools like Notre Dame, which will play for the national championship on Jan. 7 against Alabama, and Stanford — is a more curious case. The Huskies, who earned a bid to the Jan. 1 Orange Bowl, are a surprise both on and off the field.
How did Northern Illinois finish so high? The New America rankings are not just based on raw statistics like graduation rates or the NCAA's Academic Progress Rate, which indicate how well a team is keeping its players on track to graduate. If that were the case, a school such as Notre Dame, which graduates 83% of its players, according to federal data, would finish well above Northern Illinois, which has a 66% rate.
(VIDEO: How a D.C. High School Football Team Beat All Odds)
Instead, the New America Foundation bases its rankings on several factors: how a football team's graduation rate compares to that of the school's overall male student body, how a team's black-white graduation gap compares to the male black-white graduation gap in the general student population, and the spread between a football team's black graduation rate and the school's overall graduation rate for black men. "Our formula is the only one out there that puts these statistics into context," says Alex Holt, an education researcher at the New America Foundation. (New America's formula gives less weight to a school's Academic Progress Rate, which it considers a less rigorous test, than actually graduating).
So Northern Illinois scores major points because football players graduate at a higher rate (66%) than the Northern Illinois student body at large (51%). At Northern Illinois, 72% of white players graduate, while 63% of black football players graduate: that's a nine-point difference. In the general population, 56% of white male students at Northern Illinois graduate, compared to 30% of black male students. That's a 26-point difference for the student body, compared to a nine-point difference for the football team: again, New America credits Northern Illinois football for outperforming the rest of the school. Also, while 63% of Northern Illinois' black football players graduate, just 30% of black male students graduate overall. That 33-point difference propels the Huskies to the top of the standings.
(MORE: How Notre Dame Has Lifted College Football)
On the flip side, look at the team from Michigan, a school with a strong academic reputation, yet finishes near the bottom of these rankings. While Michigan graduates 88% of its students, only 59% of Wolverine football players get their diplomas. While the black-white graduate gap on the football team is only four points worse than black-white gap for all male students, just 47% of Michigan's black football players graduate, compared with 70% of Michigan's black male students overall.
(For more details on each school in New America's study, click here for a graphical representation of the results.)
Almost all education rankings are imperfect, and New America's research is no different. In order to make comparisons with overall graduation rates on a given campus, for example, New America Foundation uses federal graduation rates in its data. College athletic departments have criticized these rates for understating an athletic team's performance, since players who transfer out of a school and pursue a degree elsewhere, or leave early for the pros, count against them. To account for athlete mobility, the NCAA came up with the "graduation success rate" (GSR), which credits teams for graduating incoming transfers, and doesn't penalize them for having players transfer out or pursue the pros. For almost all teams, the GSR is higher than the federal rate. But there is no GSR for the rest of the student body, so New America uses the federal rate to make comparisons.
(PHOTOS: Top 10 College Football Gameday Traditions)
Aside from the baseline numbers, you can certainly question a methodology that gives more credence to campus context than raw performance, which puts Northern Illinois, with its 66% federal graduation rate for football, above Notre Dame, at 83% (Northern Illinois has a 83% GSR, while Notre Dame's GSR is 97%). But no matter how you slice the numbers, as we go into bowl-game season, the study reminds us of the shortcomings of college sports. For 19 of the top 25 football teams — or 76% — their federal graduation rates are lower than those of the overall student population. On 22 of the top 25 college football teams — or 88% — more than 30% of the players fail to graduate. Using the more generous, and probably fair, measure — the GSR — 15 out of the top 25 college football teams (60%) fail to graduate more than 30% of their players.
That's just not a winning game plan.

subset: commoncrawl


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The Hong Kong University of Science and Technology
This course offers a conceptual framework for understanding China that highlights the intersection of politics and economics. It shows that rather than develop into a full blown market economy, state and party officials at all levels of the political system maintain significant influence in economic development. Such a "political" economy has had both positive and negative outcomes, which we will assess in detail. We also look at the origins, views, backgrounds and relations among leaders, and how those leaders make decisions about public policy and try to get those decisions implemented down through the system. China has few formal institutions through which citizens can participate in politics, but we will study the strategies Chinese people use to try to influence their leaders' decisions. Finally, we assess China's future and whether rapid economic development and the emergence of a vibrant middle class will push China towards greater democracy or whether the single party system is likely to survive into the future. The course is a quite useful background for Chinese Politics Part 2 – China and the World.
Course Overview video: https://youtu.be/7FpNL67EbE4
Specific details
Category of Education
Social Science


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Now Is a Time for Growth
It's fine to talk -- eventually -- about chronic deficits and mounting debt. But now that our government is up and running again, the nation's first priority should be economic growth.It's fine to talk — eventually — about chronic deficits and mounting debt. But now that our government is up and running again, the nation's first priority should be economic growth.
Sorry if this gives conniptions to all you deficit hawks out there. Actually, I'm not that sorry, because it was the hawks' over-the-top warnings of impending doom that provided intellectual cover for the meat-cleaver budget cuts we're living with today.
Partly because of those "sequestration" cuts — and because the economy is slowly improving — the federal government's annual budget deficit is falling at its fastest rate in decades. For the 2012 fiscal year, the deficit was about $1.1 trillion. For fiscal 2013, the Congressional Budget Office projects a deficit of $642 billion, representing a one-year decline of more than 40 percent.
This is part of a trend. The deficit peaked at $1.4 trillion in 2009 and has been sliding ever since. I don't mean to suggest that we don't have a problem. But it's clear at this point that the extraordinary deficits we saw at the height of the Great Recession were anomalous and that the flow of red ink is returning to normal. The CBO predicts that deficits will continue to fall through 2015.
What happens then? Actually, it's too early to say.
The biggest factor in the size of the deficit — and the cumulative federal debt, now at more than $17 trillion — is rising medical costs. As the huge baby-boom generation reaches retirement age, according to the budget-hawk scenario, the Medicare and Medicaid programs will eventually become so expensive that the government will have nothing left for "discretionary" spending on roads, education, medical research, social welfare, environmental protection and other necessities.
There are signs, however, that this dystopian future may not be written in stone. Ten years ago, health care spending was growing at an alarming 8.8 percent a year — far faster than the economy could possibly keep up. But since 2008, according to an analysis of federal data by the Kaiser Family Foundation, health care spending has grown by an average of just 4.2 percent a year.
Is the slowdown permanent? Unclear. Does the Affordable Care Act deserve any credit? Also unclear. The one thing that seems certain is that the slower rise in medical costs, even if it's only temporary, should give policymakers the opportunity to take a deep breath and make sensible decisions. At this point, even those who believe the sky is falling have to acknowledge that it isn't falling as quickly as they feared.
The dollar amount of the debt matters much less than its size relative to the economy. The right thing to do is work on both sides of that equation — try to keep the debt from zooming out of control while at the same time promoting economic growth.
I would go a step further and argue that given the slowdown in the rise of medical costs, we should take the opportunity to focus primarily on growth. The biggest component of the economy is consumer spending, which becomes more robust as unemployment drops. So the smart thing is to stop paying lip service and start taking action on the "jobs, jobs, jobs" agenda that everyone claims to support, Republicans and Democrats alike.
Here's one possible place to start: corporate tax reform. President Obama and the House GOP majority agree that there should be a lower corporate tax rate — without the loopholes that allow some firms to avoid paying taxes at all. Meanwhile, U.S. companies have parked nearly $1 trillion in profits overseas to avoid paying the nominal 35 percent U.S. corporate rate.
As part of a reform package, why not a conditional amnesty that lets corporations repatriate a dollar tax-free for every dollar they invest domestically in ways that create jobs?
Another target for economic growth is the energy sector. Because of the natural gas boom, the United States may soon be the largest producer of hydrocarbons in the world. Intelligent rulemaking can ensure that as the industry expands, parallel industries dedicated to safety, cleanup and alternative fuels grow with it.
And of course there's always infrastructure. I suppose we'll focus on our steel-and-concrete needs the next time a bridge falls down or a train derails.
Look, I'm not a debt-crisis denier. But I know that the problem will be much easier to fix if the economy is expanding at a robust pace. In the end, we're not going to cut our way to success. We have to grow.
Eugene Robinson's e-mail address is eugenerobinson(at)washpost.com.
© 2013, Washington Post Writers Group
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You are here
thermodynamics of nanoscale small systems
How to measure the temperature of a nanotube?
- Henry Tan's blog
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- 327590 reads
Yes, I Agree with you..
Thats no temperature..
How to hold a small system at a fixed temperature?
One way to think about temperature and a small system is to allow the small system to exchange energy with a much larger system (i.e. a reservoir of energy). The temperature of the reservoir is well defined. The reservoir is so large that, as the small system draws energy from the reservoir, the temperature of the reservoir remains unchanged.
Thus, the small system fluctuates from one quantum state to another quantum state. The probability for the small system to be in any one of its quantum state, of course, follows the Boltzmann distribution.
This picture is what we mean by saying "a system is held at a fixed temperature". In this sense, we can hold an arbitrarily small system at a fixed temperature.
I have collected my notes on temperature and the Boltzmann distribution, along with several other topics, in Statistical Mechanics. In these notes, I have deliberately treated the subject as an experimental science: all quantities must be measurable, including the number of quantum states of an isolated system. I'm particularly happy with the section on temperature. Several students have kindly mentioned to me that they appreciate this attitude.
Operational definitions of temperature rely on thermal contact
At a basic level, defining temperature of any system requires thermal contact, namely, exchanging energy between systems. Here is the definition of the absolute temperature T
1/T = change in the logarithm of the number of quantum states divided by the change in the energy of the system, everything else being fixed.
All relative temperature scales are also defined via thermal contact. So far as I know, there is no operational definition of temperature other than those based on thermal contact.
Informal definition of temperature
Henry, Zhigang's explanation of temperature is spot on. However, if you want another "intuitive" notion regarding temperature of, say a nanotube (which you quoted), then you may think of temperature as the measure of the velocity or kinetic energy of the atoms. In fact, this notion is used to compute the temperature of a molecular dynamics ensemble. While at the level of each atom, all you can calculate is its kinetic energy, when you have an ensemble, statistical mechanics provides a route to compute the so-called temperature.
Sure, for very small number
Sure, for very small number of atoms, stat mech may not be the solution but I am speaking of physical intuition. While the concept of "hotness" etc. are somewhat useless at that scale, relating temperature to the degree of motion of an atom provides an intuitive understanding of what temperature means at that scale
Mr Tan, But it
Mr Tan,
But it should make sense, as the molecules/atoms vibrate or move around, they do so because they have velocity. And when we talk about molecular dynamics wont we say KE = (1/2)mv2 where KE = (3/2)NkT (for a 3D system, K - Boltzmann's constant?)
Then we do have energy and thus 'temperature'.
Re: statistical meaning of temperature
In teaching a course last spring, I updated my notes on temperature. The central aim of the notes is to reconcile the empircal notion of temperature and its statistical meaning. Hope that the notes help.
quantum states and the fundamental postulate
The fundamental postulate is also intriguing. It says that a system isolated for a long time is equally probable to be in any of its quantum states. That our world is described by quantum states may be regarded as a law itself.
Thermodynamics of irreversible processes
These are excellent questions, but generally useful answers do not exist. They belong to nonequilibrium phenomena.
For one class of nonequilibrium phenomena, the system is not in equilibrium as a whole, but the system can be divided into small elements, each element being in a state of equilibrium. One can follow the thermodynamics of irreversible processes to anaylze how the system as a whole approaches a state of equilibrium.
A classical example is conduction of heat in a solid. While the entire body is not in a state of equilibrium, each small element of the body is in its own state of equilibrium. It is not meaningful to talk about the temperature of the entire body, but one can talk about the temperature of each element of the body, and apply the equilibrium thermodynamics to every element. One then describes the conduction of heat by using a kinetic law (i.e., Fourier's law).
As another example, in my course on advanced elasticity, I describe nonequilibrium phenomena in gels.
Quantify a notion through its experiemntal consequence
We may have entered the muddy water of philosophy of science, of which I'm not qualified to comment, but I agree with Zhenyu, if a notion has no measurable consequence, you may not be bothered to define it. If a notion does have experimental consequence, it might be possible to define a quantity through experimental consequence.
The notion of hotness can be quantified through the experimental consequence of thermal contact.
- In the case of two macroscopic systems, we can talk about the temperature of either system.
- In the case of a small system in contact with a heat reservoir, however, we do have a well defined way to characterize the system: the Boltzmann distribution.
The textbook definition of temperature
Dear Henry: I wish this were my definition. This is the definition in textbooks. For example, in Kittel and Kroemer, and in Landau and Lifshiz. A while back I wrote a fanatic short review of K-K. It was that book that made me "see" the subject.
I'm not entirely sure why you insert "average" in the above definition.
I'm imagining a system that can exchange energy with the rest of the world, while all other modes of interaction are blocked. Thus, the system is not an isolated system. However, when the energy of the system is held at a constant value U, the system becomes an isolated system, and has a certain number of quantum states Ω. As the energy changes, the number of quantum states changes as a function of the energy, Ω(U). This function characterizes a family of isolated systems.
For example, an electron and a proton form a hydrogen atom. The two-particle system can absorb energy by receiving photons. Thus, the system may be viewed as a family of isolated systems. According to quantum mechanics, the function Ω(U) takes the following values:
Ω(-13.6 eV) = 2, Ω(-3.39 eV) =8, Ω(-1.51 eV) = 18,...
For a large system, the discreetness in energy is small compared to the total energy, so that U may be treated as a continuous variable, and Ω(U) may be treated as a continuous function. In this case, an analysis of thermal contact leads to the definition of temperature:
The unit of temperature was discussed elsewhere in this thread.
Thank you, Henry, for initiating this thread of discussion. As you pointed out, the subject is really hard. I'm not sure if I have got everything correct. Please do point out if you find that I'm doing things wrong.
On the validity of S = S1 + S2
Dear Henry:
You probably mean to write
N=N1 x N2.
So when S = log N, you will have
You put your finger on an important point. In an introductory discussion of thermal physics, we analyze system in weak interaction, so that N=N1 x N2 is true. As I discussed in my notes on temperature, physically it means that all the interfacial states are negligible.
In your example, you have two electrons, so that the "interfacial state" is all you get, not negligible. In such case, we have no reason to assume N=N1 x N2.
But this is not the end of the game. Any time you get an interfacial phenomenon, you will violate N=N1 x N2. You will introduce excess quantities.
I'm not sure how to deal with your 2 electrons, though.
Extensive vs. non-extensive entropy
I'll keep it short (lest I am off-the-mark). The additivity of entropy S = S1 + S2 assumes extensivity, whereas for systems that interact/exhibit long-range interactions (gravitational field is an example), the notion of entropy has been generalized to describe such non-extensive systems. Such entropic measures (Renyi, Tsallis and others are well-known) lead to non-extensivity, and the presence of an additional term (S = S1 + S2 + S1*S2*(1-q)). Tsallis statistics as it has come to be known is purported to be a generalization of Gibbs-Boltzmann statistics. Tsallis's entropic measure is non-extensive when q is not equal to 1 (q = 1 reduces to Shannon's measure). Tsallis entropy has received (for and against) much attention in the physics literature and also in areas outside it (networks, turbulence, finance, etc.) and it is used to describe many a complex systems (edge of chaos) that exhibit power-law distributions. An article that appeared in Science summarizes the gist of it all; Tsallis's original article appeared in 1988. So, instead of the Shannon entropy measure, use of Tsallis's non-extensive entropic measure in Jaynes's maximum-entropy formalism has been pursued.
Nanotubes present no challenge to statistical thermodynamics
As discussed above, you can hold arbitrarily small system at a fixed temperature by letting the small system exchange energy with a heat reservoir. In doing experiment with a nanotube, perhaps a holder will allow the nanotube to exchange energy with the environment.
I'm not familiar with how calculations are carried out, but at least conceptually and in experiments, nanotubes and such present no fundamental challenge to statistical thermodynamics.
No need to define T for isolated systems
Reading through this line of discussions, I will have to agree with Zhigang (and some others), in the sense that there is even no need to be bothered by how the temperature should be defined for truly isolated systems, be they classical/macroscopic or quantum (such as those containing only very few numbers of elemental entities). Such systems, treated typically using microcanonical ensembles, are fully described by physical quantities such as the total (and conserved) energy, the volume, etc., with no specification of the temperature.
T claims its physical identity when a system is exchanging energy with its outside world, but by then the system is no longer isolated.
---Just some stochastic thoughts while fighting a cold and fever...:)
What about Thermodynamic Laws in Nano Scale?
I heard some things about Nano-Scale Thermodynamics Law?
What's the state of Thermodynamic laws in nano-scale?
Violation of the 2nd law in nano-scale
Although this interesting discussion that I have tried to follow is not in my particular field, the current point has reminded me a paper published by the American Physical Society in 2002.
This is the paper just in case you have not seen:
Wang et al., "Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales", Physical Review Letters 89, 050601 (2002).
Here is another one:
Carberry et al. "Fluctuations and Irreversibility: An Experimental Demonstration of a Second-Law-Like Theorem Using a Colloidal Particle Held in an Optical Trap", Physical Review Letters 92, 140601 (2004).
Best regards,
Alper Erturk
Temperature of nanotubes and Prof. Suo's notes...
Some comments, in no particular order...
Prof. Zhigang Suo points out that temperature and energy have the same dimensions. This is an insightful statement, but requires certain qualifications to be made.
1. The equivalence between the two concepts is obtained after assuming many prior assumptions. It might be interesting to trace the route through which the equivalence is obtained.
First, a primarily kinetic description of the system is assumed. The system is taken to primarily consist of moving point-masses; let's call them particles. The motion of the particle is taken to remain restricted to a certain finite region of space. The total number of particles in the region may be taken to stay unchanged over any length of time. The collisions with the bounding surface usually are taken to be "perfectly" elastic.
The reason the particle is taken as a point-mass is that by doing so, the internal structure of the particle can be treated as of no consequence to the statements made within the framework of the theory. The same assumption also does away with any theoretical complications arising due to the spatial extents of the mass, e.g., complications due to moments, directions in collisions, etc.
Note that we talk about the mass and energy *of* the system. In other words, we do make meaningful statements about the system in and by itself, i.e., even if there is nothing outside of it. Thus, something outside of the system is not necessary to impart meaning to a given system itself or to any of its properties. In particular, no external reservoir is necessary to define temperature of the system.
The system here is identified as the sum total of the masses and their motions within a particular spatial region, together with the boundaries of the region and the special properties of the boundary such as the perfectly elastic collisions they give rise to.
Provided conditions such as above are met, even the entire universe can be taken, in an abstract sense, to be an isolated system. In any case, it's worth noting that every isolated system is actually an abstraction.
2. If the kinetic theory of matter (e.g. the atomic hypothesis of Dalton) is applied to a thermodynamically macroscopic system, then, completeness requires that every macroscopic property have some description in the kinetic-theoretic terms as well.
The kinetic-theoretical concept equivalent to temperature in thermodynamics turns out to be the *kinetic* energy of particles (e.g. atoms).
Note, only the kinetic energy is involved here, potential energy in any of its forms is not. The reason is that the kinetic theoretical abstraction primarily omits any form of interaction between the constituent particles making up the system.
Now, the above manner is not how actual atoms or subatomic particles behave. The small broken pieces of matter such as atoms (and, electron, protons, neutrons, even quarks...) do interact with the other small pieces. But this fact is against the spirit of the kinetic theory.
The interaction between particles is the fundamental reason why real gases deviate from the ideal gas law. It also is one fundamental reason why the temperature<->energy equivalence has only a limited, i.e. qualified, validity.
3. Note, temperature is primarily a property of the system--not of its constituents.
However, as a result of the fact that there can be no interactions among constituents, the simple additivity rule can be assumed. Hence, it is possible to linearly subdivide a given system into a number of constituent *systems.*
The constituent systems may conveniently be built so as to isolate a single particle, e.g. an atom.
It is then that one may ascribe a temperature to a single constituent, e.g., an atom.
4. Note, by the premises of kinetic theory, it really does not matter whether the system description carries one particle or N particles.
Even a subsystem may carry any number of particles. If the decomposition is not in integral terms, it's even permissible to think of a subsystem as carrying a fractional number of particles.
The kinetic abstraction itself is silent on these issues and its structure is equally applicable to all such possibilities.
5. Let's apply the above principles to a concrete case. Consider a moving car. It is possible to think of an abstract system consisting of this car and nothing else in the world.
If this abstract system is taken to exchange no matter or energy with anything else, then it can be taken as an isolated system. (Note, isolated systems are necessarily abstractions.)
Inasmuchas the car may be represented as a point-mass in an abstract system, it is also permissible to ascribe a "temperature" to that system.
Note, the actual hotness of the car (say due to its running engine), or the possibility of measuring it using a thermometer, has been summarily ignored right in the act of modeling it as a point-mass. Hence, its real temperature (say 27 degrees Celsius) does not at all enter into the discussion. The temperature of the system we mean here is the one which the car possesses by virtue of its motion--i.e. out of its kinetic energy.
Finally note, the issue is not really speaking microscopic vs macroscopic, or QM vs classical, etc. The issue is: Can you meaningfully speak of something in the terms of the kinetic theory or not, that's all.
6. If a principle that correlates the kinetic energy of a nanotube (say due to vibrations of the ionic cores and waves in the lattice gas) with something external can be discovered, then, even an experimental measurement of the temperature of the nanotube will be possible.
So, the question "Can you measure the temperature of a nanotube?" is not one ruled out by basic physical principles. It is to be answered by through developments in the experimental science.
7. To conclude:
- The description of temperature in terms of energy is not at all quite on the same footing as its description as a sensory quality.
- The temperature<->energy equivalence is not an unqualified one. Indeed, this equivalence denotes a high-level abstraction.
- Temperature is a property of the system, primarily, not of the point-masses. But the premise of composition allows us to ascribe temperature to individual entities--by assuming smaller systems encompassing the individual entities.
- Accordingly, even a single atom, electron, quark, etc. can be taken to possess a temperature. The procedure is meaningful in the above context.
- Yet, since such a description involves high-level abstractions, a certain amount of restrain must be exercised while using the term "temperature," especially when scientists make statements to lay people.
For example, the statement that a temperature of a billion K was reached in a laboratory can be careless if there is no explanatory context provided. In today's technology, such a temperature is reached only for a single constituent particle. But lay people take it to mean as if a whole assembly palpable at the gross scale was heated to that temperature. To not take the care to spell out the explanatory context is to mislead the public.
- It is alright to think of the temperature of nanoparticles even if the particles are made of only a few hundred atoms.
Temperature and energy are not equivalent
Dear Ajit: Thank you very much for your comments on my notes on temperature. I wish to reiterate a few points.
In the notes, I adopted the following definition of temperature T:
1/T = change in the logarithm of the number of quantum states divided by the change in the energy of the system, everything else being fixed.
- This temperature has the same dimension as energy.
- To preserve the notion of hotness, any monotonically increasing function of T can equally well be called the temperature.
- In particular, the SI unit asks you to rescale the above T with a linear factor, such that the triple point of a pure water is by definition 273.16K (exact). The conversion factor k (known as the Boltzmann constant), can be determined experimentally by this definition. See a website of NIST for detail of the defintion of Kelvin as a unit of temperature.
- Thus, k is a factor to convert two units of hotness, just like 2.54 is the factor to convert inch to centimeter. (If I were Boltzmann, I'd be amused to be reduced, without my knowledge, to a conversion factor!)
- Just because the two quantities have the same unit does not mean they are equivalent. I don't think that we should say that temperature and energy are equivalent. The above definition of T has made their nonequivalence quite clear.
- As outlined in my notes on temperature, the above definition does lead to experimental procedure to measure temperature, as well as measure the number of quantum states.
About equivalence...
Dear Zhigang,
It's nice that you reproduced the pertinent part of your notes for convenience of the reader's reference.
Frankly, though, I cannot understand why you wouldn't say the two are equivalent once the appropriate context was being specified. (Not necessarily the one I mentioned, but let's assume that a proper context has been given....)
IMHO, any time the physical dimensions of two quantities are identical, and the two concepts also refer to the same or similar phenomena, then the cognitive policy of theoretical integration requires that one also try and see the way in which the two concepts may be related, even equivalent.
In saying "equivalent," one still keeps the two concepts separate. The concepts still do not become "interchangeable" or "identical." Yet, there are contexts where the theoretically similar concepts are much more than being merely "analogous."
The parallels between the kinetic theory and thermodynamics (or particles and fields, speaking more broadly) is one such a context where, IMHO, it's perfectly OK to say "equivalent". On the other hand, the out-of-plane displacements of a soap membrane and the potential of an electrostatic field could never become "equivalent"--they must remain "analogous."
The basic test, I would suppose, is that in drawing theoretical parallels between two theories describing the same sphere of physical phenomena, if the two concepts go on to produce exactly the same physical effects, then, within the scope of the comparison, the two concepts should be regarded as equivalent--on the grounds that their "valence" (or capacity to produce effects) was equal.
But I suspect by now all this hair-splitting must have become positively boring, so let me stop!
It's just that your observation about the identity of the dimensions was really fine and got me thinking... It's a very fundamental point you made in your notes, and it's worth investing some thinking about... It's something like Planck's constant (having units of the physical "action") or the physical meaning of the constancy of speed of light (which Feynman asks in his Lectures to ignore through scaling, somewhat similar to the way you note Boltzmann's constant as a constant of scaling).
Before closing, let me add a word: I am new to iMechanica, being here for only about a month or so. But, it has been my pleasure to be a member here. Sometimes one does write at length. (In my case, most of the times!) Then, there are those other times when one feels like taking a shot in the dark, to be not very precise! I can understand that... In any case, the informality of a blog site preciesly is its strength! I am happy to have this chance to write more informally than in a paper, but more formally (and for a wider audience) than in a personal level talk...
So, my special thanks go to you and also to others (say the moderators) for taking this initiative...
Energy and temperature are not equivalent, really.
To see that energy and temperature are not equivalent, take a look at the following statement:
"When two systems are in thermal contact, energy goes from the system with high temperature to the system with low temperature."
If you swap the positions of the two words, energy and temperature, the statement becomes amusingly wrong.
Stick to equivalence; your example is of interchangeability...
I too initially found the example amusing but for a somewhat different reason--out of the fact that despite having clearly spelt out interchangeability as different from equivalence in my *immediately* above post, you still ask the reader of your site to consider an example of interchangeability as if it were an example of equivalence.
So, initially, I was amused.
But soon later on, I took a more serious view of it. This is the second time within a week or so that a superfluous post has been added after my entry, mandating nothing but reiterations. That too from people one would ordinarily take to be responsible, understanding and mature. I ignored the occurrence the first time, but now I must speak out.
It is this necessity to reiterate which leads me to suspect if people here consider having the last post as a prestige issue of sorts or what!
If so, I wouldn't mind being as speedy in leaving this forum as I was in joining it.
So what if it's Harvard, Stanford, or Cambridge or any other university out there! Truth, in my mind, is above all those institutions, let alone a very small community that is iMechanica. When truth becomes so easily dispensable as the click of a button and an addition of an entry just to have it as a last entry (on the lines of having the last laugh of sorts), I would have nothing to do with that kind of a forum--even if the sponsoring institution made a rather large song and dance about "VERITAS" in the logo. I could do better not to post at such a site. After all, I do have a personal Web site of my own, and Yahoo!, msnbc.com and other newsmakers *have* been following my case mindlessly for years too! So, if the whole matter is to keep praising publicly some people and to indirectly drive some others to a position that, to a casual reader, would show a lack of temperament on those others' part, then I know this is routine in Internet, but I would have none of it.
Once again, note, mindlessly adding entries not recognizing the contents of the previous posts is happenning for the second time in just one week for posts made by me. Once again, ask yourself if you are *not* giving an example of interchangeability in the name of equivalence.
Do let me know, publicly, if I should discontinue to be a member here.
That said, in the meanwhile, coming back once more, and from my side, for the last time, to the same physics as I explained right above:
If you really are consistent in holding the meanings of the terms, there indeed is no contradiction in the statement you offered at all. So, there is no reason for amusement. Consider this rephrasing of your statement (on the lines of equivalence, but not interchangeably, which simplycannot be done as I already said):
"When two systems are in thermal contact, the temperature of the system which has the higher level of kinetic energy goes down whereas the temperature for the system which has a lower level of kinetic energy goes up."
Tell me, what is wrong with this? And was is so hard to think up this example? Especially after having gone through my well explanatory post?
Let me know, on other points, publicly.
re: Stick to equivalence; your example is of interchangeability
Dear Ajit:
I have benefited from this thread of discussion. If anything that I posted has ever offended you, please accept my sincere apology. It is wholly unintentional. This message is not intended as the last word on anything. I simply feel that I should respond to your requests.
In online discussions, our intentions, unaided by facial expressions but quickened by a push of a button, may not be clear to each other. Such is the limitation of this mode of communication. One may recall the same situation in early days of emails. By now most of us have accepted that emails are less formal than snail mails.
We may think of iMechanica as an infinite hallway, where we can "meet" colleagues and discuss anything. People can express their thoughts freely, superfluous or profound or anything in between, just as in a conversation in a real hallway.
I have enjoyed your posts, including those in this thread. If you judge that the benefit of such a communication to you outweighs posts that you judge to be superfluous, then I would sincerely urge you to stay.
Now let us return to the topic of our discussion: temperature and energy. I think I see where you come from. Correct me if I have misinterpreted what you are trying to say.
For a classical gas, the temperature is proportional to average kinetic energy of particles. Indeed, for a classical gas, the temperature and the average kinetic energy are equivalent and interchangeable.
I have added the word average. I think that you would agree the word average is significant here. It makes the temperature an intensive quantity. The total kinetic energy is an extensive quantity. Thus, in thermal contact, the sum of the energies in the two systems is constant, but the sum of the temperatures of the two systems need not be constant. In equilibrium, the energies of the two systems need not be equal, but the temperatures of the two systems are equal. Even in this special case of classical gas, the temperature is not equivalent or interchangeable with total energy.
The statement you made between quotation marks will be correct if you replace the word "system" by the phrase "classical gas", and replace the the phrase "level of kinetic energy" by "average kinetic energy".
A generally applicable definition of temperature is (I apologize to repeat this again):
1/T = change in the logarithm of the number of quantum states divided by the change in the energy of the system, everything else being fixed.
This definition makes it clear that temperature involves two distinct quantities: the energy of a system, and the number of quantum states of the system. Both quantities depend on the size and the kind of the system (a piece of cheese or a glass of wine). Yet when two systems reach thermal equilibrium, the temperatures of the two systems are equal. Thus, temperature has this property that energy does not have.
Winding up my discussion in this thread for the time being...
Dear Zhigang,
Thank you for your reply.
Your apology was not necessary for a matter like this, and an apology wouldn't have been sufficient by itself either! But forget it! The way I look at it, when there is that sincerity to your words, *that* is enough by itself.
For the time being, I have decided to stay with the forum. Yet, I simply cannot be light-hearted about it; not yet. One man doesn't make a forum.
There is my experience of Americans, who often are mere power lusters but packaged in smooth or civilized appearances. Then, there are those arrogant and suppressive Harvard graduates and the companies they run that one does come across. I can cite Mr. Manu Parpia, the man, and Geometric Software, and 3D PLM Software, India, the companies he runs as a CEO. Something similar can be said for Stanford graduates too. I can directly cite Sandip Johri, V/P of Hewlette-Packard, a batch-mate of mine at COEP, and a personal friend *once upon a time*. Other examples where my dignity or my job applications or similar matters have suffered injustice or ill-treatment at the hands of Americans can be cited rather easily too. For example, at the hands of the IIT Bombay alumni in the San Francisco Bay Area (such as Mr. Jaggi Ayyangar), IITians who now are American citizens, people whose power-lust sometimes exceeds that of the American-borns themselves. (One route of harassment used by all such Americans--born in the USA or otherwise--has been by en-masse buying the staff and advertisement space in media, esp. Times of India, Pune edition. The reader may ask Dileep Padagonkar, the then editor, for more details. I am sure he knows me.)
If the reader thinks I have gone too far, he is requested to know more about my competence and skills by visiting my Web site: http://www.JadhavResearch.info, and then note that over the last 6.5 years, I have earned any money at all for precisely 5 months and a few days--not even for a half year (full six months). 6 years is a long time. People finish PhDs and buy houses in that time. Further, I have summarily been denied all my chances in CAE, despite all that hue and cry you undoubtedly hear about India's talent et cetera. (If in doubt, ask the Governor of the State of Virginia in the USA.) And this condition of mine is despite (or may be, because of) Harvard graduates. If this is not suppression, what else do you think would be?
All such factors do play a role in deciding how I should proceed with respect to anything being run by Americans or in America, the more prestigious, the more cautious I must be. (And no, all this writing about America and Americans is *not* a blanket moral certificate of better behavior by other nations or people.)
The above is not an explanation; it is as brief but direct an indication as I can at all give. (This was about third revision to make it further brief, and I cannot make the matter more condensed without losing the personal flavor about it--and then, whose decision and life is it anyways that I am talking about, here?)
Coming to the physics proper. Let me just note some thoughts without explaining them. Apparently, these points will need separate articles.
-- Any extensive property can be turned into an intensive one; simply divide by mass.
-- Your "definition" of temperature has the following roots. Start with the definition of entroy dS = deltaQ/T and Boltzmann's equation: dS = -k ln (w). (delta Q, for inexact differential.) Substitute, rearrange, and scale to remove Boltzmann's constant, k. Then, bring in the interpretation of w as in accordance with a particles approach, here and by your post, quantum states. Note, if the resulting equation is to be taken as giving us a *definition* of temperature then one already is very much within the kinetic-theoretical abstraction.
-- I note that you wish to differentiate classical gas and collection of quanta. I think this insistence is understandable but not really necessary. However, it will take a few more papers just to get going. I will publish them after my PhD thesis is done. Decades of QM developments have got it wrong, and I don't at all blame you personally (or anyone else) for honestly believing so. If anything, I appreciate your concern and the clarity of your expression.
-- I will also explain later more on equivalence in a separate post.
-- I plan not to post for a while. I plan to take my PhD thesis to a better stage of completion and then come back. May be, one week later or so.
Before closing, one more point, a clarification. This point is no reflection on Zhigang or admin or any other member at all but just a noting. Since some part of this post of mine indeed is dramatic, I want to note that if in future there arise some issues (say legal issues) for the iMechanica management out of this post, I will be only happy to leave the forum--but I will not on my own retract it. (My attitude is, and would be: "It moves!")
demonstration and satisfaction
Dear Ajit:
I understand your sensitivity. It will be a bit out of context (he is speaking of mathematics), but please take these words of T. Jefferson regarding the American approach on getting things done:
" ... We have no theories there, no uncertainties remain on the mind; all is demonstration and satisfaction."
Demonstrate your work and satisy our minds, you will be appreciated regardless of anything else.
Please keep writing here!
is the concept of photon challenged as well?
so, does this mean that you are also claiming that the concept of photons in finite-molecular/atomic systems is challenged?
Experimentally speaking, this is easier to answer since phonons are hard to observe.
Imaging Phonons
A book entitled Imaging Phonons by J. P. Wolfe should provide an excellent introduction.
More on thermodynamics of nanostructures?
I found all you discussions are very stimulating and interesting, so I would like share with you some of my thoughts, and possibly stir the water even more...
Thare have been similar dissussions on wether thermodynamics (equilibrium theory) can be applied to small systems of finite size (such as nanostructures), because they are in principle "metastable" (relative to bulk). For example, one intriguing question whether a finite system (a few atoms) ever melts? If it does, what's the melting temperature?
Temperature, as well as any other thermodynamic state variable, an statistical mean (ensemble average) of certain thermodynamic measure. In dependent of system size, such average (or measure) can always be performed (as suggested Zhigang and others). One concern is fluctuation becomes increasing bigger as the size decreases, so the deviation from the mean value increases, which sometimes makes the analysis "questionable"? For example, temperature fluctuations make the melting point ill defined.
Technically, in fact, some other thermodynamic quantities are even harder to define for the small systems than temperature. As discuss here, one may always calculate temperature by the Boltzman distribution of quantum states or avearging over kinetic energy of atoms (in MD simulation), but the volume of a finite system is in fact somewhat "arbitrary", without a definite position of boundary.
So, extending the question beyond temperature, one asks whether thermodyanics can be applied to a small system that can never be truely "equilibrated" due to large fluctuations? Nevertheless, it has been practically used so far (such as many many MD simulations) possible due to the following reasons: (1) even though metastable, their life time is so long that the nanostructures can be considered at "equilibrium"; (2) cases where fluctuations are not too large to confuse the issue; (3) There is no other better way to treat it, so we do the best we can for now...
Entropy and temperature are not concepts limited to a continuum
Dear Henry:
I'm not sure entropy and temperature are concepts for a continuum. Let us look at the entropy first. For an isolated system, the entropy is simply the logarithm of the number of quantum states of the system:
S = logΩ.
For example, a hydrogen atom can be an isolated system, and we can speak of its entropy. The values of its entropy are listed elsewhere in this thread.
A more general definition seems to belong to Gibbs. I described this definition in my notes on entropy. As I remarked in my response to Sukumar a while back, one can define entropy simply as a property of any probability distribution. Thus, one can speak of the entropy of rolling a die, or entropy of whether tomorrow will rain, for example.
For an isolated system, the fundamental postulate says that every quantum state is equally probable. Then Gibbs's definition is reduced to S = logΩ. This much I did in my notes. What I didn't have time to do in the notes was to develop this line of reasoning into a useful idea. In any case, the entropy has nothing to do with continuum.
We have talked about temperature extensively in this thread of discussion. In particular, one way to hold a small system at a fixed temperature is to allow it to exchange energy with a reservoir of energy. In this picture, one does not speak of the temperature of the system, but speaks of the fluctuation of the system among various quantum states.
As an ancient example of a small system, consider a vacancy in a crystal lattice. We hold the vacancy to a fixed temperature simply by holding the crystal at a fixed temperature. The vacancy can trade energy with the crystal. We can then speak of various states this vacancy is in, e.g., whether it is energetic enough to move to another lattice site.
Perhaps a key to apply thermal physics to small systems is to carefully define an excess quantity. For it is not obvious how to privatize energy to a vacancy. Which part of the energy belongs to the crystal, and which part of the energy belongs to the vacancy?
How can we use the concept of temperature for few atoms
Very interesting topic!
I read the first parts of the book Thermal physics written by C.Kittel under the suggestion of Prof. Suo. I post this comment to explain what I learn form that book.
First, the thermal contact plays a signifcant role in the definition of the temperature and entropy. As for two systems, we can obtain the total degeneracy of all the accessible configurations after the thermal contact. If the number of particles in at least one of the two systems is very large, the numbers of that total configurations can be replaced by the number of the states in the most probable configuration. Only in this case, the additivity of the entropy is valid.
As defined in the lectures of Prof. Suo:1/T = change in the logarithm of the number of quantum states divided by the change in the energy of the system, everything else being fixed. The introduction of temperature is to describe the equilibrium state of two systems under thermal contact. It is noted that this equilibrium state is just the most probable configuration. The formalism of T is also derived from the maximum of total degeneracy of all the accessible configurations. In this sense, we can think T is corresponding to the most probable configuration. However, the states expect the most probable configuration can be observed only when the number of particles in at least one of the two systems is very large. If the two systems are both small, then we can see that many different states expect of the most probable configuration which can be represented by the temperature.
Thus, for a small system with only few atoms, we can define the temperature of this kind system via letting it contact with a very large system. However, when we make two small systems together, how can we obtain the final temperature of these two systems, even though we know the temperature of them before contact. If we make they contact with a large system, this may destroy the states of the real systems and make them have the same temperature of the large system itself.
I am not sure whether my understanding is reasonable or not, however, I hope this can make any help for this topic.
Best regards
Teng Zhang
temperature without thermal contact
For an isolated ergodic Hamiltonian system with kinetic energy quadratic in the momenta (all standard assumptions), there is a clear definition of the temperature based on the derived result of equipartition. This does not require the notion of thermal contact for the definition, and an entropy for such a system can be defined (non-extensive) to be consistent with the macroscopic thermodynamic relation between reciprocal temperature and the derivative of the entropy w.r.t energy.
Now how well this definition corresponds with the 'level of hotness' we physically perceive, and think we measure and also think as understand as temperature, that I have not decided in my mind with certainty (I think the question may be undecidable), but there is a clear definition to hang on to without involving thermal contact.
From having skimmed over this voluminous thread, it seems that many here do not like this definition (most must be aware of it since this is a standard notion?).
I would like to know any thoughts on this anyone might have.
Incidentally, in the attachment to the post
I summarize some basic statistical mechanics in the microcanonical ensemble, all learnt from the book by Berdichevsky referred to in the paper.
I recommend the book highly to students of mechanics - Berdichevsky, being a student of Sedov's and having degrees in both solid and fluid mechanics writes like a mechanician, and after a long search I finally found a book where the fundamentals are laid out clearly - no philosophy. He also makes the connection between statistical mechanics in the microcanonical and canonical distributions in the limit of large N and there are nice connections with when fluctuations become important, a fact that can be captured by working in the microcanonical setting.
- Amit
I skimmed over much of this discussion, but I would suggest you read up on the work of the pioneers in this field, e.g. Terrell Hill, Ali Mansoori, also possibly Gian Beretta's thermodynamics
textbook, and his work on single particle system quantum thermodynamics variables,
if I remember correctly. Here's a starter page:
Also authors who publish on so-called violations of the second law are all individuals who have never read Clausius' textbook and are aiming to disprove the Boltzmann version of the second law:
Re: Nanothermo: Thermodynamics of small isolated systems
An interesting paper on this subject was published by Mandelbrot in 1962. Check out
The Role of Sufficiency and of Estimation in Thermodynamics
Benoit Mandelbrot
Source: Ann. Math. Statist. Volume 33, Number 3
(1962), 1021-1038.
The purpose of this paper is to point out (and to
use) the relations of certain statistical concepts with "statistical" thermodynamics.
(A) It is observed that Gibbs's "canonical distribution"of energy is precisely what statisticians have later labeled a "distribution of the exponential type". It follows that a rigorous treatment of the canonical law can be based upon the concept of "sufficiency", which is thereby related to the physical idea of "thermal equilibrium" and to the "zero-th principle of thermodynamics". In other words, the theory of physical fluctuations can be based upon "principles" very similar to those of the "phenomenological", or "classical, non-statistical" thermodynamics. Naturally, our results will be less detailed than those of statistical mechanics. However, the foundations of the latter theory still raise a host of unanswered
problems, and it seems good in the meantime to show that the less powerful phenomenological theory has a wider scope than is commonly thought (see also [15]). The possibility of a purely phenomenological approach to statistical thermodynamics is not in itself a new idea. A procedure somewhat similar to ours has indeed been long ago suggested in Szilard's admirable, but very difficult and neglected, paper [18]--not to be confused with his [19]. Of course, Szilard used a quite different vocabulary; but, with hindsight, one may now say that he has co-invented the concept of sufficiency with R. A. Fisher; by showing that, under certain regularity conditions, Gibbs's canonical law is the only probability distribution with a single scalar sufficient statistic, Szilard also anticipated the results of G. Darmois [2], B. O. Koopman [10] and E. J. G. Pitman [16], but was partly anticipated by Poincare [17].
(B) The second thesis of the paper is independent of Szilard, and concerns the concept of temperature. For systems with a canonical
energy, the temperature is the parameter of the Gibbs distribution; as such it is undefined for isolated systems with a determined energy. However, it is necessary to generalize the concept of temperature to isolated systems. Several definitions have been proposed and, although they all safely converge mutually for the usual very large systems, the temperature remains athematically ambiguous for small isolated systems; it also becomes physically meaningless. We shall show that the temperature for systems-in-isolation should be viewed as a statistical estimate of the parameter of a conjectural canonical distribution, from which the presently isolated system may be presumed to have once been drawn. This interpretation explains the nature of the ambiguity of the concept of temperature; it also meets the actual practice of physicists; finally, some of the a priori conditions, which the physicists impose upon their "estimators", turn out to correspond to the statistical conditions of consistency, unbiasedness, and efficiency. Physicists also use two very interesting variants of consistency and unbiasedness, which we shall study under the names of "self-consistency" and "self-unbiasedness". The most commonly used temperature, due to Ludwig Boltzmann, turns out to be the maximum likelihood estimator. In summary, we hope to show that it is a great pity that mathematical and physical statistics should have developed largely independently of each other, while using the same concepts. By combining the rigor of modern statistics with the intuitive vigor of thermodynamics, both should be served well. However, as things stand, the mathematical statistician should not hope to unearth in the literature of physics any result as yet unknown to him. An important open problem suggested by this paper is the following. When sufficiency and estimation are defined in the most general terms, it seems that one should also be able to generalize the scope of thermodynamics. However, an approach such as that of P. R. Halmos and L. J. Savage [5] could not be applied to thermodynamics without substantial restrictions, as we shall show in Section 7. It remains to study these restrictions in greater detail, before one can assert that a non-void generalization of thermodynamics is possible. The problem is addressed to both mathematicians and physicists. We shall strive to reduce to the minimum the detailed knowledge of physics required to read this paper. If the reader's appetite for information about thermodynamics has been awakened, he could do no better than to make use of references [11] and [20].


text:
Note: This announcement was updated with information about deadline extension for single-choice early action applications.
The University campus will be open tomorrow, Thursday, Nov. 1. Only critical and essential employees are required to report to work. University buildings and facilities will be accessible for students, faculty and staff who need to use them. Staff who support key operations will be contacted directly regarding their work requirements.
The University's Tiger Transit system will resume limited operations Thursday, from 8 a.m. to 10 p.m.
Graduate students, faculty and staff are welcome to use Dillon Gym, Firestone Library and Frist Campus Center. Most University services are running on fall recess schedule.
Unless otherwise indicated, all weekend events will be held as scheduled. Some events may have been cancelled, so those who plan to attend or participate in events should check the event listing online or contact the respective event coordinators.
Several key roads that lead to the campus are open, but many roads remain closed. Traffic conditions can be monitored through Google traffic or 511NJ, but please note that these independent sites vary in functionality.
Power to University buildings that are not connected to the University's cogeneration system, including Stanworth Apartments and Butler Apartments, will be restored when the public electricity supply is back up.
Some campus buildings that have been running on power from the University's cogeneration plant may lose power briefly when they are switched back to the public electricity supply.
For the latest information on power status for campus operations, check the Department of Facilities' "outage" page.
University Services and Tiger Transit also will provide graduate, undergraduate students and members of the campus community with bus service to Princeton Shopping Center from 10 a.m.-4 p.m., Thursday, Nov. 1. The bus, listed as the shopper on TransLoc, will start with the first trip at 10 a.m. and then run continuously beginning at 12 p.m., with the final trip back to campus at 4 p.m.
The stops would be as follows: Stanworth Apartments, Graduate College, Princeton Station (Dinky), Lawrence Apartments, Butler Apartments, and Princeton Shopping Center.
The bus will bring shoppers back from the shopping center via Stanworth Apartments, Graduate College, Princeton Station (Dinky), Lawrence Apartments, and Butler Apartments.
Because of Hurricane Sandy, the Office of Admission is extending the single-choice early action deadline for all students to Nov. 7. All applications must be submitted online or postmarked by this date unless personal or hurricane-related issues make it difficult or impossible to file the appropriate forms.
This extension also applies to students who are submitting applications through the QuestBridge process. The financial aid deadline for early action remains Nov. 10. For any counselors, teachers or recommenders who may be affected by the hurricane, the Office of Admission will be flexible on the submission of school forms and supporting documents.


text:
Liquid Crystals
Liquid crystals are sometimes referred to as the "fourth state" of matter following gases, liquids, and solids. The individual molecules flow past each other as they do in a liquid but tend to be oriented in the same manner, like the molecular arrangement in a solid crystal. However, the molecular forces maintaining the liquid crystal state are sufficiently weak that it can be maintained only over a limited range of temperatures and pressures. If the liquid crystal substance becomes too cold, it reverts to an ordinary solid. If it becomes too hot, it reverts to an ordinary liquid. It is also easily affected by changes in mechanical stress, electromagnetic fields, and chemical environment. Although it displays characteristics of both a crystal and a liquid, the liquid crystal state also has properties that are unique.
Not just an artificial contrivance, this phase occurs naturally and is found in biological systems, organizing and condensing processes such as the formation of chromosome and cellular membranes.
Liquid crystal behavior was first observed between 1850 and 1888 by researchers in chemistry, biology, medicine and physics. They observed that the optical properties of certain materials changed discontinuously with increasing temperatures. During 1922 in Paris, France, Georges Freidel suggested the classification scheme, which is used today with different phases of liquid crystals called smectic, nematic, and cholesteric.
Since the 1960s, a variety of applications incorporating liquid crystals have been developed, ranging from "mood rings" to simple thermometers and complex display screens for computers. The future promises to replace cathode ray tube TVs and computer monitors with liquid crystal displays. Another technology under development involves "switchable" windows that can be changed from clear to opaque with the flip of a switch.


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There were solid increases in home prices during the month of February across all 20 major cities where that data is tracked, according to the latest S&P/Case-Shiller Home Price Indices report.
"Despite some recent mixed economic reports for March, housing continues to be one of the brighter spots in the economy," economist David Blitzer, who directs the work done by S&P Dow Jones Indices, says in the report.
Some of the data:
-- The average home price in the 20 cities rose 9.3 percent from February 2012 to February 2013.
-- From January to February alone, prices rose 0.3 percent.
-- "Phoenix continued to stand out with an impressive year-over-year return of 23 percent."
-- There were also significant year-over-year price increases in Las Vegas (17.6 percent), Atlanta (16.5 percent) and Detroit (15.2 percent).
Bloomberg News says the report is another sign that "the U.S. housing market is strengthening."
Copyright 2020 NPR. To see more, visit https://www.npr.org.


text:
It's not that I don't care about being thin and gorgeous, it's...wait. No, actually, that IS it. I don't care. So imagine my delight when I discovered the latest lunch craze hitting our nation's bakeries:
Yep, these lunch-sized portions of cake come with everything you need for a nutritious meal: sugar, fat, more sugar, and most importantly: a handy fork for on-the-go eating!
No more sneaking into the breakroom in search of cutlery! No more sharing with the kids! Now you can consume your Porta-Pastry as God intended: hunched over the steering wheel in your car, crying.
"Just a second, kids; Mommy's just finishing her lunch."
So far the baking industry has just been testing the market with their Watermelon Porta-Pastry, but happily the response has been so positive they're preparing to introduce a new design:
Thanks to Annabeth C., Lauren K., Alden L., Jennifer L., Shannon B., and Jane D., who think that lousy Aflac duck had it coming.


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How Does Mitt Romney Stop Rick Santorum's Rise?
What's the best way for Mitt Romney to stop Rick Santorum?
For the answer, we went to someone who has done it before.
Democratic strategist Saul Shorr helped Bob Casey defeat then-Sen. Santorum, R-Pa., in a landslide in 2006. Santorum lost by 18 points.
But Shorr says that was a general election; in a Republican primary, Romney will have a much harder job.
"Here's Romney's challenge ... in a lot of these primaries you're dealing with an electorate that's made for Santorum," Shorr says. "They have questions about Romney's conservatism, and they don't have any questions about Santorum's.
"Look, when Romney's folks took out Newt Gingrich ... it was really like shooting fish in the barrel."
Unlike Gingrich, Shorr says, Santorum isn't a target-rich environment. But Charlie Black, an outside adviser to the Romney campaign, isn't so sure. He says people are overestimating Santorum's surge.
"The polls you see right now reflected the bounce, the halo effect he got from winning three nonbinding events last week," Black says. "Santorum really hasn't had a glove laid on him yet, but his record and his position on the issues will be examined now."
The Romney team is just getting started with millions of dollars in ads in many of the upcoming primary states, including Romney's native state of Michigan, where a loss to Santorum would be humiliating.
The ads define Santorum as a friend of K Street and as a big spender.
Deflecting Attacks
The Santorum campaign is trying to inoculate itself against the assault with its own ad that shows an image of Santorum dodging a mudslinging rifle attack.
"We're not going to sit back and take incoming from the Mitt Romney campaign that's dishonest and untruthful and negative. That's not what the country wants to hear," says Hogan Gidley, Santorum's national communications director. "I think they've roundly rejected that to this point, as you can tell by Mitt Romney's troubling favorable ratings while Rick Santorum sits in the 70 percentile."
In Michigan, for instance, Santorum's favorable ratings are much higher than Romney's — 67 percent to 49 percent, according to Public Policy Polling. And that's why Richard Land, the head of the Southern Baptist Convention's Ethics and Religious Liberty Commission, says Romney needs to be careful.
"If he starts trying to attack Rick personally, the way he attacked Newt [Gingrich], it's going to be like, you know, big mean Mitt jumping all over the choir boy," Land says. "There could be a real backlash."
Reaching Conservative Voters
There's something else fueling Santorum's rise.
Social issues have returned to the debate thanks to President Obama's decision to require contraceptive coverage at religiously affiliated institutions. Land says that gives Santorum an edge.
"People know about Romneycare and they know that it was similar to Obamacare, and when the president takes off his mask and we see the ugly business end of government coercion, as we did last week, it reminds social conservatives of what's at stake," Land says.
In a Republican primary, Romney can't run to Santorum's left by arguing that Santorum is too conservative to beat Obama — even if that may be true. And, unlike Gingrich or even Rick Perry, Santorum doesn't offer Romney much room on his right.
Going Positive
Shorr thinks the Romney campaign is in a tough spot.
"I'm sure that they're poring over their polling, really trying to look for where to go against Santorum. Yes, he can try to paint Santorum as an insider in Washington, but he's really an insider of the corporate suite," Shorr says. "I just think that's a tough sell, and in some way shape or form, it may be that Romney's positive ads are going to matter as much as anything else."
Now that's an odd notion — that, this year, positive ads could make the difference. But plenty of Republicans say Romney has to do more to lay out a positive vision for the future. One way or another, Romney adviser Black is still counting on the candidate's superior resources.
"You're going into a period where the race becomes more national. There are actually 13 events including in some large states in the next three weeks," Black says. "One reason that Romney has withstood the challenge of four or five or six candidates already is he has a national political organization and a national fundraising organization. Nobody else does."
Black predicts that Romney's organization and money will prevail in the upcoming states. It's certainly true that when Romney has brought this advantage to bear, he has won — see Florida. When he hasn't spent big, he has lost — see Colorado, Missouri and Minnesota.
But it might take more than financial advantage for Romney to regain his front-runner status.
Correction Feb. 9, 2012
Previous audio and Web versions of this story incorrectly said that Mitt Romney had lost the Nevada caucuses. In fact, he won Nevada but lost Colorado, Missouri and Minnesota.


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The farmers market was absolutely overflowing with cheap local blueberries this weekend and I picked up a lot of them. Although I will finish a lot of them off for breakfast on plain yogurt with a touch of maple syrup, I wanted to do something with them and I knew exactly what. I had been wanting to try doing a cinnamon bun stuffed with fruit or berries and I had originally planned on trying it with strawberries but they disappeared just before I got the chance and a blueberry version now sounded even better. The idea was basically to make cinnamon buns and where you add blueberries to the cinnamon layer before rolling them up. I figured that wild blueberries would be perfect for these cinnamon buns as they were smaller and rolling them up would be easier. I could have just gone with that but I kept thinking about how much I like the blueberry and maple flavour combination and so I decided to replace the sugar in the cinnamon layer with maple sugar and I then mixed some maple syrup into the cream cheese glaze. While I was adding things, I could not resist also adding some chopped pecans which also pair well with blueberries.
The blueberry maple pecan cinnamon buns turned out so amazingly well! I really liked how the blueberries in the cinnamon layer baked up in the buns with many of them bursting and spreading their blueberry goodness even further. The blueberry, maple pecan flavour combination was definitely a winner and it went perfectly in the light and fluffy buns. You can bake the cinnamon buns in several different ways to get different results. You can either leave them with lots of room to spread out when they bake or you can pack they in tightly next to each other to get thicker buns. I baked most of mine in a spring form pan and I put the extras in ramekins and the ones that were baked in the ramekins were my favourites by far.
Blueberry Maple Pecan Cinnamon Buns
- 1 recipe basic sweet yeast dough (see below)
- 1/2 cups maple sugar (or white or brown)
- 2 teaspoons cinnamon
- 1 cup wild blueberries
- 1/2 cup pecans (toasted and chopped)
- 1 batch maple cream cheese glaze (see below)
- Punch down the dough. and knead for 30 seconds.
- Cover the dough and let it rest for 10 minutes.
- Roll out the dough on a floured surface into a 24″ by 12″ rectangle.
- Mix the sugar and the cinnamon and sprinkle it onto the dough followed by the blueberries and pecans.
- Roll the dough into a log and pinch and cut it into 12 even slices.
- Arrange the buns in a greased pan, cover in plastic wrap and let rise until doubled in size, about 1 hour and 30 minutes.
- Bake in a 375F/190C preheated oven until golden brown, about 15-20 minutes.
- Top the buns with the glaze and enjoy.
Basic Sweet Yeast Dough
- 1/4 cup water (warm)
- 1 tablespoon active dry yeast
- 1 teaspoon sugar
- 1/3 cup sugar
- 2 eggs (room temperature)
- 1/3 cup butter (melted)
- 1/2 cup sour cream (room temperature)
- 1 teaspoon vanilla extract
- 1 teaspoon salt
- 3 1/4 cups flour
- Mix the water, yeast and sugar into a large bowl and let it sit until foamy, about 10 minutes.
- Add the sugar, eggs, butter, sour cream, vanilla, salt and 2 cups of flour and mix for 2 minutes at medium or 200 strokes by hand.
- Stir in enough of the remaining flour to make a soft dough.
- Place the dough onto a lightly floured surface and knead the dough until smooth, about 5 minutes. (The dough should feel soft and buttery and not sticky.)
- Place the dough in a greased the bowl, cover with a damp towel and let the dough rise until it has doubled in size, about 1 hour and 30 minutes.
Maple Cream Cheese Glaze
- 4 ounces cream cheese
- 1/4 cup maple syrup (or to taste)
- Beat the maple syrup into the cream cheese until it reaches hte desired consistency.


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Conn. Police Find 'Very Good Evidence' On Gunman
The massacre of 26 children and adults at a Connecticut elementary school elicited horror and soul-searching around the world even as it raised more basic questions about why the gunman, a 20-year-old described as brilliant but remote, was driven to such a crime and how he chose his victims.
Investigators were trying to learn more about Adam Lanza and questioned his older brother, who was not believed to have been involved in the rampage at Sandy Hook Elementary. Police shed no light on the motive for the second-deadliest school shooting in U.S. history.
In tight-knit Newtown on Friday night, hundreds of people packed St. Rose of Lima Church and stood outside in a vigil for the 28 dead - 20 children and six adults at the school, the gunman's mother at home, and the gunman himself, who committed suicide. People held hands, lit candles and sang "Silent Night."
"These 20 children were just beautiful, beautiful children," Monsignor Robert Weiss said. "These 20 children lit up this community better than all these Christmas lights we have. ... There are a lot brighter stars up there tonight because of these kids."
Lanza is believed to have suffered from a personality disorder and lived with his mother, said a law enforcement official who was briefed on the investigation.
Asked at a news conference whether Lanza had left any emails or other writings that might explain the rampage, state police Lt. Paul Vance said investigators had found "very good evidence" and hoped it would answer questions about the gunman's motives. Vance would not elaborate.
The tragedy plunged the picturesque New England town of 27,000 people into mourning.
"People in my neighborhood are feeling guilty about it being Christmas. They are taking down decorations," said Jeannie Pasacreta, a psychologist who volunteered her services and was advising parents struggling with how to talk to their children.
Lanza shot his mother, Nancy Lanza, drove to the school in her car with at least three of her guns, and opened fire in two classrooms around 9:30 a.m. Friday, law enforcement officials said, speaking on condition of anonymity.
A custodian ran through the halls, warning of a gunman, and someone switched on the intercom, perhaps saving many lives by letting them hear the chaos in the school office, a teacher said. Teachers locked their doors and ordered children to huddle in a corner, duck under their desks or hide in closets as shots reverberated through the building.
The well-liked principal, Dawn Hochsprung, was believed to be among the dead. A woman who worked at the school was wounded.
Maryann Jacob, a clerk in the school library, was in there with 18 fourth-graders when they heard a commotion and gunfire outside the room. She had the youngsters crawl into a storage room, and they locked the door and barricaded it with a file cabinet. There happened to be materials for coloring, "so we set them up with paper and crayons."
After what she guessed was about an hour, officers came to the door and knocked, but those inside couldn't be sure it was the police.
These 20 children lit up this community better than all these Christmas lights we have ... There are a lot brighter stars up there tonight because of these kids
Monsignor Robert Weiss
"One of them slid his badge under the door, and they called and said, `It's OK, it's the police,"' she said.
A law enforcement official speaking on condition of anonymity said investigators believe Lanza attended the school several years ago but appeared to have no recent connection to it. It was not clear whether he held a job.
At least one parent said Lanza's mother was a substitute teacher at the school. But her name did not appear on a staff list. And the official said investigators were unable to establish any connection so far between her and the school.
Lanza's older brother, 24-year-old Ryan Lanza, of Hoboken, N.J., was questioned, and investigators searched his computers and phone records, but he told law enforcement he had not been in touch with his brother since about 2010.
For about two hours late Friday and early Saturday, clergy members and emergency vehicles moved steadily to and from the school. The state medical examiner's office said bodies of the victims would be taken there for autopsies.
The gunman forced his way into the kindergarten-through-fourth-grade school, authorities said. He took three guns into the school - a Glock and a Sig Sauer, both semiautomatic pistols, and a .223-caliber Bushmaster rifle, according to an official who was not authorized to discuss information with reporters and spoke on the condition of anonymity. The weapons were registered to his slain mother.
Lanza and his mother lived in a well-to-do part of prosperous Newtown, about 60 miles northeast of New York City, where neighbors are doctors or hold white-collar positions at companies such as General Electric, Pepsi and IBM.
His parents filed for divorce in 2008, according to court records. His father, Peter Lanza, lives in Stamford, Conn., and works as a tax director for GE.
The gunman's aunt Marsha Lanza, of Crystal Lake, Ill., said her nephew was raised by kind, nurturing parents who would not have hesitated to seek mental help for him if he needed it.
"Nancy wasn't one to deny reality," Marsha Lanza said, adding her husband had seen Adam as recently as June and recalled nothing out of the ordinary.
Catherine Urso, of Newtown, said her college-age son knew the killer. "He just said he was very thin, very remote and was one of the goths," she said.
Lanza attended Newtown High School, and several news clippings from recent years mention his name among the honor roll students.
Joshua Milas, who graduated from Newtown High in 2009 and belonged to the school technology club with him, said that Lanza was generally a happy person but that he hadn't seen him in a few years.
"We would hang out, and he was a good kid. He was smart," Joshua Milas said. "He was probably one of the smartest kids I know. He was probably a genius."
The mass shooting is one of the deadliest in U.S. history, and among school attacks is second in victims only to the 2007 Virginia Tech massacre, which left 33 people dead, including the gunman. Reaction was swift and emotional in Newtown and beyond.
"It has to stop, these senseless deaths," said Frank DeAngelis, principal of Colorado's Columbine High School, where a massacre in 1999 killed 15 people.
In Washington, the Coalition to Stop Gun Violence organized a vigil at the White House, with some protesters chanting, "Today IS the day" to take steps to curb gun violence. In New York's Times Square, a few dozen people held tea lights in plastic cups, with one woman holding a sign that read: "Take a moment and candle to remember the victims of the Newtown shooting."
President Barack Obama's comments on the tragedy amounted to one of the most outwardly emotional moments of his presidency.
"The majority of those who died were children - beautiful little kids between the ages of 5 and 10 years old," Obama said at a White House news briefing. He paused for several seconds to keep his composure as he teared up and wiped an eye. Nearby, two aides cried and held hands.
Australian Prime Minister Julia Gillard described the attack as a "senseless and incomprehensible act of evil."
"Like President Obama and his fellow Americans, our hearts too are broken," Gillard said in a statement.
In Japan, where guns are severely restricted and there are extremely few gun-related crimes, the attack led the news two days before parliamentary elections. In China, which has seen several knife rampages at schools in recent years, the attack quickly consumed public discussion.
In Newtown, Robert Licata said his 6-year-old son was in class when the gunman burst in and shot the teacher. "That's when my son grabbed a bunch of his friends and ran out the door," he said. "He was very brave. He waited for his friends."
He said the shooter didn't utter a word.
Kaitlin Roig, a teacher at the school, said she implored her students to be quiet.
"I told them we had to be absolutely quiet. Because I was just so afraid if he did come in, then he would hear us and just start shooting the door. I said we have to be absolutely quiet. And I said there are bad guys out there now and we need to wait for the good guys to come get us out," Roig told ABC.
"If they started crying, I would take their face and say, `It's going to be OK. Show me your smile,"' she said. "They said, `We want to go home for Christmas. Yes, yeah. I just want to hug my mom.' Things like that, that were just heartbreaking."