Irreversible thermodynamics of fluids

Irreversible thermodynamics of fluids is formulated based on a set of postulates. The theory thus constructed generalizes thermostatics and linear irreversible thermodynamics into the realm of nonlinear irreversible processes. In this theory the extended Gibbs relation and the entropy balance equation appear as a pair of mutually consistent equations under the postulates made. An equivalent theory is also formulated by replacing one of the postulates with another that is basically a variational principle. The variational principle yields the evolution equations for fluxes as the Euler equations that extremize the variational functional postulated. The local form of the extremized variational functional is the entropy balance equation for the irreversible processes in the system. Some further consequences of the theory are also considered. For example, nonequilibrium specific heats are shown to be at least quadratic functions of fluxes and reduce to the equilibrium specific heats in the limit of vanishing fluxes. In order to illustrate an example of possible applications, we have considered nonlinear transport processes in fluids. The connections of the present theory with other theories are discussed.