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I tried to check this in google scholar but didn't find a paper explicitly focused on this topic. Do anyone know of some references on this issue? I do not mean the thermodynamics in curved spacetime which is well covered by Tolman's book ``Relativity, Thermodynamics and Cosmology''.

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    $\begingroup$ can you please elaborate why you think the curvature of space-time will at all effect the statistics? I mean locally every curved space is euclidean. So local equilibrium will not be affected at all. $\endgroup$
    – Ari
    Commented Mar 8, 2016 at 14:41
  • $\begingroup$ I am mostly interested in the merit of general covariance and statistical physics. Since we know we need the energy spectrum or Hamilton to write down the partition function(functional if for fields) which must based on a 3+1 decomposition. $\endgroup$
    – Wein Eld
    Commented Mar 8, 2016 at 14:51
  • $\begingroup$ Related: physics.stackexchange.com/q/110763/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Mar 8, 2016 at 14:52
  • $\begingroup$ @Ari, Furthermore, for the very early universe, we can not take the view that every small piece of space is almost flat. $\endgroup$
    – Wein Eld
    Commented Mar 8, 2016 at 14:52
  • $\begingroup$ @Qmechanic, Thanks very much, Qmechanic. The post you recommended is also useful to me. But it is still different from my question anyway. $\endgroup$
    – Wein Eld
    Commented Mar 8, 2016 at 14:59

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