Heat, work, and the thermodynamic temperature at nonequilibrium steady states

Abstract

We continue our investigation of the properties of matter at nonequilibrium steady states using a thermodynamic formalism derived from molecular fluctuations. Based on the generalized Clausius inequality, we extend the definition of ‘‘reversible’’ process to include transformations between steady states and relate reversible work and heat to changes in state functions. The variable which is thermodynamically conjugate to the internal energy, that is, the inverse of the generalized thermodynamic temperature, is an integrating factor for the reversible heat. We discuss the relationship of the generalized temperature to the Kelvin temperature, how the generalized intensive variables can be measured, define generalized heat capacities, and obtain the Gibbs–Duhem relationship satisfied by the intensive variables. These ideas are illustrated for two simple steady state systems, a fluid under homogeneous shear and a two level gas which is pumped by radiation. Finally we analyze under appropriate conditions the electromotive force of a chemical reaction system held at a nonequilibrium state. We predict corrections to the Nernst equation which depend on how far the chemical reactions are removed from equilibrium.