An entropy current in superspace

We construct a consistent entropy current from which a hydrodynamic entropy current can be extracted using a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating function. The consistent entropy current can be defined quantum mechanically by coupling it to an external source. We find that the consistent entropy current is given by the bottom component of an entropy current superfield which is conserved in superspace, but when restricted to real space satisfies a non-conservation law. Our analysis is valid in the probe limit which allows us to fully treat quantum fluctuations of the theory.