Non-equilibrium statistical field theory for classical particles: Basic kinetic theory

TL;DR

This paper applies a non-equilibrium field theoretical approach to classical particle ensembles, deriving macroscopic evolution equations from microscopic dynamics, and linking classical kinetic theory with field theory.

Contribution

It demonstrates how the non-equilibrium field theory reproduces classical kinetic equations and connects microscopic particle dynamics to macroscopic evolution, including the BBGKY hierarchy.

Findings

Recovered continuity and Jeans equations for free particles.

Derived BBGKY hierarchy from the field theoretical approach.

Established a link between classical and field-theoretical kinetic descriptions.

Abstract

Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy (BBGKY hierarchy) with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.