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Black Brane Entropy and Hydrodynamics

A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics of higher dimensional black holes. This Letter introduces a correspondence between phenomenologically defined entropy currents in relativistic hydrodynamics and quasilocal horizons of near-equilibrium black objects in a dual gravitational description. A general formula is given, expressing the divergence of the entropy current in terms of geometric objects which appear naturally in the gravity dual geometry. The proposed definition is explicitly covariant with respect to boundary diffeomorphisms and reproduces known results when evaluated for the event horizon.