  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.
