Mesoscopic thermodynamics of stationary states

A thermodynamics for systems at a stationary states is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density ans its conjugated nonequilibrium chemical potential as a mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker-Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes we derive nonequilibrium equations of state.