Generalized Grad-type foundations for nonlinear extended thermodynamics.

Abstract

The maximum-entropy formalism provides an exponential ansatz, \ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{}, for the phase-space distribution that can be used in the information-theoretic entropy functional to calculate nonequilibrium thermodynamic potentials. \ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{}, like the Grad function, gives a finite number of moments exactly. If \ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} is used to derive a Gibbs equation, the thermodynamic pressure is not in general one-third the trace of the momentum flux, as commonly assumed phenomenologically. One can modify the exponential ansatz by adding terms. Coefficients in these terms satisfy physical conditions such as requirements that thermodynamic pressure and entropy flux have their classical forms. These conditions alter the thermodynamic forces. However, in terms of the new forces, one can modify the projection operator of Grabert to derive a set of nonlinear extended thermodynamic kinetic equations exhibiting Onsager symmetry. Depending on conditions imposed, one has statistical bases for several equivalent forms of nonlinear extended thermodynamics.