Abstract
We find a (quasi)local first law of thermodynamics, $\mathrm{\ensuremath{\Delta}}E=T\mathrm{\ensuremath{\Delta}}S\ensuremath{-}W$, connecting gravitational entropy, $S$, with matter energy and work. For Einstein gravity, $S$ is the Bekenstein-Hawking entropy, while for general theories of gravity, $S$ is the Wald entropy, evaluated on the stretched future light cone of any point in an arbitrary spacetime, not necessarily containing a black hole. The equation can be written as $\ensuremath{\rho}\mathrm{\ensuremath{\Delta}}V=T\mathrm{\ensuremath{\Delta}}S\ensuremath{-}p\mathrm{\ensuremath{\Delta}}V$ by regarding the energy-momentum tensor as that of a fluid.
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