  In hydrodynamics the existence of an entropy current with non-negative
divergence is related to the existence of a time-independent solution in a
static background. Recently there has been a proposal for how to construct an
entropy current from the equilibrium partition function of the fluid system. In
this note, we have applied this algorithm for the charged fluid at second order
in derivative expansion. From the partition function we first constructed one
example of entropy current with non-negative divergence upto the required
order. Finally we extended it to its most general form, consistent with the
principle of local entropy production. As a by-product we got the constraints
on the second order transport coefficients for a parity even charged fluid, but
in some non-standard fluid frame.
