Relativistic Boltzmann equation and relativistic irreversible thermodynamics

Abstract

The covariant Boltzmann equation for a relativistic gas mixture is used to formulate a theory of relativistic irreversible thermodynamics. The modified moment method is applied to derive various evolution equations for macroscopic variables from the covariant Boltzmann equation. The method rigorously yields the entropy differential which is not an exact differential if the system is away from equilibrium. Therefore, an extended Gibbs relation does not hold valid for the entropy density in contrast to the usual surmise taken in extended irreversible thermodynamics. However, an extended Gibbs relation-like equation holds for the compensation differential as has been shown to be the case for nonrelativistic gas mixtures in a recent work. The entropy balance equation is cast into an equivalent form in terms of a new function called the Boltzmann function. The equation is seen to be a local expression of the H theorem. Macroscopic evolution equations (i.e., generalized hydrodynamic equations) are presented for various macroscopic variables. Together with the equivalent form for the entropy balance equation, these macroscopic evolution equations form a mathematical structure for a theory of irreversible processes in relativistic monatomic gases.