Kengo Shimada, Susumu Okazawa, Satoshi Iso
We give a modified derivation of the Einstein equation of state by considering the Clausius relation $T\delta S-\delta N =\delta Q$ on a null hypersurface with a non-vanishing expansion ($\theta \neq 0$), i.e. not in the {\it equilibrium}. The derivation is made possible by choosing a special observer and adding an entropy production term $\delta N$ in the Clausius relation. The interpretation of the thermodynamic relation is given based on the Noether charge method. We also extend the analysis to $F(R)$ gravity, and argue that the thermodynamic interpretation of space-time inevitably depends on a choice of observers.
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http://arxiv.org/abs/1206.1154
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