that gravity is an emergent phenomenon and one should be able to associate gravitational entropy with the (un- known) microscopic degrees of freedom underlying the spacetime geometry. Somewhat ironically, while it is possible to obtain the full set of Einstein’s equations from an entropy maxi- mization procedure [5], it is not easy to apply this tech- nique to a restricted class of metrics (like the maximally symmetric spacetimes) and obtain the relevant equations of motion in that context. Such a restriction works nat- urally only in the case of static spacetimes. So this idea works very well, for example, for de Sitter universe (which can be expressed in a static coordinate system) but not in general. I will now discuss to what extent one may be able to use the thermodynamic perspective of gravity and link the cosmic arrow of time to the direction of increasing gravitational entropy. In ref. [7], I introduced a defi- nition for entropy S associated with a two-surface, ∂ V , bounding a three-volume V , in static spacetimes with a horizon, by (see eq. (2) of ref. [7]): systems. But one can easily accommodate such an insta- bility in the behavior of the universe. The cosmic expan- sion is just a run-away solution fed by the instability. Second, this idea ties up (i) the origin of cosmic arrow of time to (ii) the quantum to classical transition made by the universe during its evolution. As we said before, nor- mal lab systems do not spontaneously evolve into a more and more classical state (in the sense of, say, the Wigner function becoming more and more sharply peaked around the classical trajectory) as time evolves. But this is pre- cisely what systems with unbounded Hamiltonians do. For example, the inverted harmonic oscillator in Eq. (3), treated as a quatum system, is known to become more and more classical as it evolves [3]. More generally, suppose we decompose the spatial 3- metric in the form g$_{αβ}$ = a $^{2}$h$_{αβ}$ with det h = 1 as a gauge condition. Using the form of Einstein-Hilbert La- grangian, one can show that while the kinetic energy term for a ( t ) has the wrong-sign, the other degrees of freedom, represented by h$_{αβ}$ , have the correct sign. In other words, it is only the overall scale factor which has an instability. Hence it is this mode which turns classical first during the evolution. If these features are maintained in the ef- fective quantum-corrected description of gravity, then we can hope to have an explanation for a broader question: Why is the classical universe described by a single dy- namical degree of freedom, rather than by, say a Bianchi type-I model with three degrees of freedom? In addition to the cosmic arrow of time determined by the dynamics of the expansion factor, we also have another well-known arrow of time, determined by the di- rection of increase of entropy. The question arises as to whether the cosmological dynamics can be given a ther- modynamic interpretation so that the expansion of the universe can be linked to the growth of gravitational en- tropy. Obviously the answer depends on the definition used for the gravitational entropy and one idea — origi- nally due to Penrose [4] — is to relate the gravitational entropy to Weyl curvature, C ab ij . Since C ab ij = 0 for the Friedmann universe and becomes non-zero as inhomo- geneities develop, this approach links the cosmic arrow of time with the direction of increasing gravitational en- tropy. This approach, however, requires us to move outside the realm of Friedmann model; that is, a strictly Fried- mann model will remain a zero entropy (or constant en- tropy) system in this framework even though the expan- sion does give it a cosmological arrow of time. From this perspective, it may be nicer if we can define the gravi- tational entropy in some other — meaningful — way so that one can work within the framework of Friedmann models without having to introduce the inhomogeneities. That such an interpretation should be possible is in- dicated by the fact that the Einstein’s equations them- selves can be obtained from an entropy maximization principle [5]. There has also been extensive work relating the Friedmann equations to the thermodynamic identity T dS = dE + PdV and its variants [6]. All these suggest This was obtained and discussed in detail in Ref. [7]. When combined with Eq. (6), this result can be expressed as the ‘equipartition law’ Δ E = (1 / 2)( k$_{B}$T loc )Δ n for mi- croscopic degrees of freedom located in the area elements of ∂ V . Alternatively, one can obtain Einstein’s equations from Eq. (8) by reversing the steps. (In fact, all these work for a wider class of theories called Lovelock gravity, of which Einstein’s theory is a special case; see [8]). For example, in the case of deSitter universe (which has a well-defined thermodynamics [9] and a static coordinate representation with a horizon) discussed in ref.[7], this procedure is straightforward. Here a i = u $^{j}$∇ $_{j}$u i = (0 , ∂ $^{µ}$N/N ) is the acceleration of the x µ = constant observers with four-velocity u $^{i}$, N is the lapse function with N = 0 representing the hori- zon H with temperature T = | κ | / 2 π where | κ | is the magnitude of the surface gravity. (The issue of signs in these expressions is discussed in ref.[7].) The sec- ond equality in Eq. (6) identifies the number of (micro- scopic) degrees of freedom in an area element √$_{σ d}$ $^{2}$x to be dn = √$_{σ d}$ $^{2}$x/L2 P and the local Unruh temperature related to the acceleration to be T loc ≡ ( N | a $^{µ}$n$_{µ}$ | ) / 2 π . Using the expression for active gravitational mass-energy defined by (see eq. (8) of ref. [7]) the Komar-Tolman in- tegral: where ¯ T$_{ab}$ ≡ ( T$_{ab}$ − 1 $_{2}$T g$_{ab}$ ) and using Einstein’s equations one can immediately obtain the relation T S = ∫$_{∂}$ V √$_{σd}$ $^{2}$x 4 L 2 P ( N | n$_{µ}$a $^{µ}$| 2 π ) ≡ 1 4 ∫$_{∂}$ V dnT$_{loc}$ (6) E = 2 ∫ V d $^{3}$x √ γN ( ¯ T$_{ab}$u $^{a}$u$^{b}$) (7) S = E 2 T ≡ 1 2 βE (8) 3