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arXiv · 1206.1154

The Einstein equation of state as the Clausius relation with an entropy production

Kengo Shimada·Susumu Okazawa·Satoshi Iso
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Abstract

We give a modified derivation of the Einstein equation of state by considering the Clausius relation $TδS-δN =δQ$ on a null hypersurface with a non-vanishing expansion ($θ\neq 0$), i.e. not in the equilibrium. The derivation corresponds to choosing a specific observer to the hypersurface, and such a generalization gives a hint how we can improve the original derivation by Jacobson. We also give an interpretation of the thermodynamic relation based on the Noether charge method.

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Kengo Shimada, Susumu Okazawa, Satoshi Iso. 2012-10-10. The Einstein equation of state as the Clausius relation with an entropy production. https://doi.org/10.1016/j.physletb.2012.10.010

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