Irreversibility in classical kinetic theory: retardation of interaction and distribution functions

TL;DR

This paper derives a kinetic equation for point particles that incorporates interaction retardation, explaining irreversible behavior without probabilistic assumptions by using retarded potentials.

Contribution

It introduces a deterministic kinetic equation accounting for interaction retardation, advancing the understanding of irreversibility in classical kinetic theory.

Findings

Equations describe irreversible particle behavior without probabilistic hypotheses

Retarded potentials incorporate field effects into many-particle dynamics

The approach provides a deterministic foundation for irreversibility

Abstract

A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the retardation of interactions between particles. The obtained equations describe the irreversible behavior of a system of particles without involving any probabilistic hypotheses. The use of the retarded potentials, in this case, corresponds to taking the field into account when the dynamics of the many-particle system is described.