Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics by Byung Chan Eu

Author:Byung Chan Eu
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

© Springer International Publishing Switzerland 2016

Byung Chan EuKinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics10.1007/978-3-319-41153-8_2

2. Relativistic Kinetic Theory of Matter and Radiation

Byung Chan Eu1

(1)Department of Chemistry, McGill University, Montreal, QC, Canada

Byung Chan Eu

Email: [email protected]

The relativistic kinetic theory of irreversible processes in a system of matter presented in Chap. 1 of this volume is generalized to include radiation in this chapter.1 The generalization enables us to remove the awkwardness inherent to the nonrelativistic theory of radiation and matter reported in the paper [1] by Eu and Mao and provides kinetic theory foundations for the relativistic irreversible thermodynamics and radiation hydrodynamics for a system of radiation and matter. In this chapter, the relativistic Boltzmann equations—more precisely, a relativistic theory (covariant) form of the Boltzmann–Nordholm–Uehling–Uhlenbeck equations [2–4]—is employed to formulate a theory of transport processes in a system of radiation interacting with matter in a manner consistent with the laws of thermodynamics.

The motivations to have a covariant kinetic theory are following: Since photons are inherently relativistic, the relativity principle requires that governing equations of the system must be Lorentz covariant. In Ref. [1] the nonrelativistic kinetic theory was used to study irreversible processes in a system of radiation interacting with matter and, in particular, to study Doppler shift corrections for photon frequencies, but the nonrelativistic kinetic theory treatment of the subject matter was found often cumbersome and awkward. It was also difficult to make sure that the definitions of statistical mechanical formulas for macroscopic variables and the evolution equations indeed had correct nonrelativistic limits. These weaknesses can be assuredly removed if a covariant theory is formulated. Secondly, there are some problems, especially, in the study of the early epoch of the universe and also in the nuclear physics of high energy heavy ion collisions, for which a relativistic formalism is required since post-collision particles move at high speed. It will be shown that the present covariant kinetic theory recovers all the nonrelativistic evolution equations in correct forms with proper relativistic connections and thus verifies the previous nonrelativistic formulation [1]. In any case, in the present chapter we formulate a relativistic kinetic theory for a monatomic gas mixture interacting with photons treated relativistically and quantum mechanically. In the kinetic equations for molecular particles and photons, the collision terms are so modified as to make them more suitable for quantum particles. Since the collision terms in the kinetic equations used in the present chapter are quantum mechanical, they naturally affect the dissipation terms of nonconserved variables in the evolution equations, but we are, nevertheless, able to make use of the approach taken in Chap. 1 of this Volume except for some details related to the quantum collision terms. As a matter of fact, the affected parts of the theory turn out to be all related to transport coefficients originating from the collision terms in the kinetic equations. Therefore, most of evolution equations involved in the theory remain the same as those in Chap. 1 of this Volume except for the dissipation terms and quantities related to them.

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