  In the hydrodynamic regime of field theories the entropy is upgraded to a
local entropy current. The entropy current is constructed phenomenologically
order by order in the derivative expansion by requiring that its divergence is
non-negative. In the framework of the fluid/gravity correspondence, the entropy
current of the fluid is mapped to a vector density associated with the event
horizon of the dual geometry. In this work we consider the local horizon
entropy current for higher-curvature gravitational theories proposed in
arXiv:1202.2469, whose flux for stationary solutions is the Wald entropy. In
non-stationary cases this definition contains ambiguities, associated with
absence of a preferred timelike Killing vector. We argue that these ambiguities
can be eliminated in general by choosing the vector that generates the subset
of diffeomorphisms preserving a natural gauge condition on the bulk metric. We
study a dynamical, perturbed Rindler horizon in Einstein-Gauss-Bonnet gravity
setting and compute the bulk dual solution to second order in fluid gradients.
We show that the corresponding unambiguous entropy current at second order has
a manifestly non-negative divergence.
