Kinetic foundation of extended irreversible thermodynamics

Abstract

In this paper we investigate the kinetic foundation of extended irreversible thermodynamics via the moment method. First we consider the construct of the 1-particle distribution function f in terms of its moments by maximizing the entropy density function. We then project f from its L2 space onto the local thermodynamic variables z=(z1,…,zN) in the thermodynamic base space B̂N. Thus instead of the Boltzmann equation we consider a set of evolution equations of z in B̂N. Second, we formulate the laws of thermodynamics governing the variable z in B̂N. These laws exhibit an intrinsic geometric structure of thermodynamics in the setting of contact geometry. Finally, as an illustration, we discuss the evolution equations for the bulk pressure Pb, heat flux Q, and the symmetric traceless tensor π⇊ corresponding to the viscous and heat conduction irreversible processes. These equations can be formulated as an abstract inhomogeneous hyperbolic evolution equation. By employing the C0 semigroup technique, we discuss the solution of the evolution equation and its asymptotic behavior. We show that thermodynamic stability condition of the system implies asymptotic dynamical stability of the solution and vice versa.