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

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.