Entropy Current for the Fluid/Gravity Model of the Chiral Magnetic Effect

We construct long wavelength asymptotically locally AdS_5 spacetimes with slowly varying (background) gauge fields which are solutions to the U(1)^n Einstein-Maxwell-Chern-Simons system. These bulk spacetimes are dual to (3+1)-dimensional fluid flows with n anomalous currents in the presence of external electromagnetic fields. We utilise the area form on the outer horizon to holographically compute an entropy current for the dual fluid to first order in boundary derivatives. Our resulting expression contains additional terms proportional to the vorticity and magnetic field and thus provides holographic confirmation of the entropy current calculated by Son and Surowka for hydrodynamics with triangle anomalies. We then restrict our bulk metric to describe the fluid/gravity model of the chiral magnetic effect (CME) and again holographically obtain the entropy current. As expected, our calculation replicates the result produced using standard hydrodynamic/thermodynamic arguments.