ON THE RELATION BETWEEN THERMODYNAMIC TEMPERATURE AND KINETIC-ENERGY PER PARTICLE

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 = T(K) = (2/3Nkappa) [K], where K is the kinetic energy. T is the temperature recorded by a thermometer in thermal equilibrium with the system. In extended thermodynamics, T(K) - 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 T(K) - 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 [K] plus results from earlier extended thermodynamic treatments of these processes. In the cases considered, far enough from equilibrium for nonlinear effects, T(K)/T - 1 less-than-or-similar-to 0.01. In other cases where we do not know how to calculate thermodynamic forces, there are consistency tests of the assumption T congruent-to T(K).