2 we argue in [1] that many other coarse-graining methods for dynamics must make implicit use of the telescoping down process. You can make your method work by care- fully analyzing your time-scales, and then making sure you know how to telescope back out to the experimen- tal situation you want to emulate. It helps to do this in terms of dimensionless variables. However sometimes you can’t compress the hierarchy to a computationally achievable regime without bringing some time-scales too close to each other, or even switching the order of time- scales. It is then a matter of subtle judgement if the be- haviour that comes out of your simulation is physically correct. inated by diffusion, you would map onto your physical diffusion time. A consequence of this strategy is that a single simulation can map onto many different physical times. E.g. if your colloid has a radius a = 1 µm , then the diffusion time is τ$_{D}$ = 5 s , and that fixes the time-scales for your simulation. On the other hand, if your colloid has a radius a = 100 nm , then τ$_{D}$ = 5 × 10 $^{$_{−}$3}$s and the ex- act same simulation would have a different fundamental time-scale. That means that for example the viscosity in your simulations would be different depending on what colloid size you were mapping to, even though the fun- damental physics is the same. This fact suggests that physical viscosity is often not such a good parameter to try and fit to in a coarse-grained simulation. You can also correctly map the same simulation to dif- ferent time-scales even though the colloidal system is un- changed. Say that you are interested in the longer-time behaviour of the velocity autocorrelation function that is dominated by the kinematic time τ$_{ν}$ . In that case if you mapped to a physical system with a = 1 µm , the times would be quite different from what you would get when you mapped to the diffusion time of the same sys- tem. So here the viscosities etc... would have different values depending on what you processes were focusing on. This is a good example of a no free lunch theorem. If you coarse-grain dynamics, you almost always need to do some kind of telescoping down, and that means that it is hard to simultaneously match multiple time-scales in your system. A similar analysis can be used to interpret systems where the dynamics are dominated by energy barriers. It is going to be very hard to know what the real physical time-scales are here because processes depend exponen- tially on barrier heights. In a coarse-grained dynamical simulation, it may be advantageous to dramatically lower (free) energy barriers in order to speed up the simulation. The hope is that you keep the relative order that charac- terizes the physical system you want to emulate, so that at least the qualitative dynamic effects are correct. But if, say, you try to interpret your time-scales from a mea- surement of single particle diffusion, and then use that time to extract a physical time for a different process in your simulation that is dominated by energy barri- ers, then you will get those numbers completely wrong. Clearly, there are many tricky subtleties that arise when trying to coarse-grain the dynamics of soft-matter sys- tems. The particular example described here concerns a col- loid in suspension where it is relatively straightforward to work out what all the time-scales are. Nevertheless, [1] J. T. Padding and A. A. Louis, Phys. Rev. E. 74 , 031402 (2006). [2] J. K. G. Dhont, An Introduction to the Dynamics of Col- loids , Elsevier, Amsterdam, (1996).