Since we are interested in a general imperfect fluid, entropy is locally not conserved and its local evolution can be given in the form of entropy density s as ∂ ∂ s ∂ ∂ t + ∇ ∇ ⋅ ⋅ J s = ∂ ∂ s c ∂ ∂ t where ∂ ∂ s c / ∂ ∂ t is the rate of increase in entropy density due to the irreversible processes of equilibration occurring in the fluid and J s is the entropy flux.