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I have recently been delving into Quantum gravity related material... and I came accross a paper by Ted Jacobson "Thermodynamics of Spacetime: The Einstein Equation of State" http://arxiv.org/abs/gr-qc/9504004 and as far as I understand the argument it is very impressive who would have thought that three seemingly unrelated theories could be so closely tied (GR, thermo and QFT). But I have two questions:

1) Why starting from the 2nd law which assumes an arrow of time can we extract a theory which is time reversal invariant GR? (this is probably closely related to the work of Hawking which I am unfamiliar with)

2) His interpretation of heat puzzles me:

specifically he identifies [tex]Q[/tex] (the heat) with [tex]T^{\alpha\beta}[/tex] (the energy momentum tensor.)"In thermodynamics, heat is energy that ﬂows between degrees of freedom

that are not macroscopically observable. In spacetime dynamics, we shall

deﬁne heat as energy that ﬂows across a causal horizon."

cheers

M