Manifestly covariant classical correlation dynamics I. General theory

Abstract

n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to the general relativity especially an application to self-gravitating systems.Comment: 19 pages, 1 figure, substantially extende

Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture

“…Unfortunately, he encountered principal difficulties when he proceeded further to derive the general kinetic equation explicitly. Such a big gap was filled in the first of this series of papers (denoted as Paper I) by the developed manifestly covariant classical correlation dynamics [23]. One of the main subjects of the present paper is to recover various special transport equations systematically from the exact, manifestly covariant and closed kinetic equation 1 found in Paper I, which we call the general transport equation.…”

“…For the evolution parametrized by τ , see Eq. ( 5), the correlation dynamics analysis may be performed for a large class of realistic systems [23]. First, we define the following distribution vectors,…”

Geometric field theory and weak Euler–Lagrange equation for classical relativistic particle-field systems

“…We emphasize that it is of significant theoretical and practical value to put the physical laws governing the classical particle-field system into geometric forms. The compact geometric forms, or manifestly Lorentz invariant forms, are especially suitable for analysis in statistical mechanics for relativistic plasmas [7,[10][11][12][13][14][15][16][17][18]. They also serve as the theoretical foundations for developing Lorentz covariant algorithms [19] for numerical simulations.…”

Sobre la termodinámica estadística de algunos sistemas relativistas y modelos cuánticos simples

“…En trabajos recientes C. Tian [66] basado en el formalismo de acción a distancia encuentra una ecuación de Liouville manifiestamente covariante con un sólo tiempo, a partir de la cual puede obtenerse como un caso particular la ecuación de Boltzmann como la primera ecuación de una jerarquía infinita de ecuaciones, además de ecuaciones más generales y todas las correlaciones entre las distribuciones de más una partícula.…”