Entropy current and equilibrium partition function in fluid dynamics

Existence of an entropy current with non-negative divergence puts a lot of constraints on the transport coefficients of a fluid, so does the existence of equilibrium. In all the cases we have studied so far we have seen an overlap between these two sets of constraints. In this note we shall try to explore the reason for such an overlap. We shall also see how a part of the entropy current could be determined from the equilibrium partition function.