Thermodynamics at nonequilibrium steady states

This work continues a discussion of how to extend equilibrium thermodynamics to nonequilibrium steady states. The extension is based on molecular fluctuations of the extensive variables and gives rise to a state function, called the σ function. The σ function reduces to the entropy at equilibrium and can be constructed from a knowledge of the local equilibrium entropy and the molecular fluctuations. The σ function depends on all the variables characterizing a steady state, including fluxes of the extensive variables and reservoir parameters. The theoretical analysis of nonequilibrium fluctuations predicts that the σ function is related to stability and the kinetics around a steady state just like the entropy is at equilibrium. Calculations of the σ function are outlined for several multicomponent systems of experimental interest. Using the fluctuation–dissipation theory, a generalization of the Clausius inequality is obtained. This leads to a class of extremum principles at steady state for Legendre transformations of the σ function.