  We propose, in the framework of the fluid/gravity correspondence, a
definition for a local horizon entropy current for higher-curvature
gravitational theories. The current is well-defined to first order in fluid
gradients for general gravity actions with an algebraic dependence on the
Riemann tensor. As a detailed example, we consider five-dimensional
Einstein-Maxwell theory with a mixed gauge-gravitational Chern-Simons term. In
this theory, we construct the proposed entropy current on a charged black-brane
background, and show that it has a non-negative divergence. Moreover, a
complete correspondence between the charged black-brane horizon's dynamics and
the hydrodynamics of an anomalous four-dimensional field theory is established.
Our proposed entropy current is then found to coincide with the entropy current
of the anomalous field theory fluid.
