Transport coefficients and temperature definition

Abstract

In the framework of classical theories on transport coefficients in fluids, based on the (generalized) Boltzmann equation, the influence of different temperature definitions in terms of microscopic quantities-such as used in the theory of Bogolubov, Choh and Uhlenbeck and in the correlation function method- is investigated. This is done by using an extension of the Chapman-Enskog method for the solution of the generalized Boltzmann equation, given by L. Garcia-Colin, M. S. Green and F. Chaos. It is found that only the integral equation and subsidiary conditions for the component of the single particle distribution function, which determines the bulk viscosity, depend on the choice of temperature definition. The integral equations for the bulk viscosity in the different theories, although rather different in form, are shown to be equivalent. Due to the difference in subsidiary conditions the quantities called bulk viscosity are different. The connection between these quantities is given. It is further argued that the temperature definition used in the correlation function method is the same as in irreversible thermodynamics, where the phenomenological transport coefficients are introduced, and that, therefore, the expression for the bulk viscosity obtained in the correlation function method is the correct one.