The fluid/gravity correspondence relates hydrodynamic flows in d dimensions to black hole dynamics in d+1 dimensions. 

It is an extension of black hole thermodynamics, where the conserved charges and the Bekenstein-Hawking entropy are upgraded into local currents.

I will propose a definition for a local current of black hole entropy relevant to higher-curvature gravity. The definition is based on Wald's formula for the global entropy in equilibrium. As examples, I will consider curvature-squared gravity, as well as 5d gravity with a U(1) gauge field and a gravitational Chern-Simons term.