On the relation between thermodynamic temperature and kinetic energy per particle

Abstract

In a computer simulation of a steady state in a fluid far from equilibrium, one needs to calculate temperature that is held constant. In classical thermodynamics and the local equilibrium approximation to nonequilibrium thermodynamics, T = TK ≡ (2/3Nκ) [Formula: see text], where [Formula: see text] is the kinetic energy, T is the temperature recorded by a thermometer in thermal equilibrium with the system. In extended thermodynamics, TK – T is of the order of squares of the heat and particle fluxes, shear-rate, or chemical reaction rate. Explicit estimates are made here of TK – T for binary isotopic diffusion, heat flow, steady Couette flow, and a classical model of a dissociation reaction. We use the maximum entropy formalism to calculate [Formula: see text] plus results from earlier extended thermodynamic treatments of these processes. In the cases considered, far enough from equilibrium for nonlinear effects, [Formula: see text]. In other cases where we do not know how to calculate thermodynamic forces, there are consistency tests of the assumption [Formula: see text].