  We construct an entropy current using a supersymmetric formulation of the
low-energy effective action for the Schwinger-Keldysh generating functional. We
define an entropy current quantum mechanically by coupling it to an external
source. It 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.
