Probability-free foundation of continuum mechanics equations irreversibility: connection with particle dynamics

TL;DR

This paper derives a new equation for the irreversible evolution of local density in a continuous medium, based on microscopic dynamics and interaction retardation, without statistical assumptions, generalizing classical fluid motion equations.

Contribution

It introduces a probability-free derivation of continuum mechanics equations that accounts for particle interaction retardation, linking microscopic dynamics with macroscopic irreversibility.

Findings

Derived a new equation for local density evolution without statistical hypotheses.

Connected the new equation with dynamic density functional theory.

Explored particular cases and implications for fluid dynamics.

Abstract

An equation describing the irreversible evolution of the local density of a continuous medium without involving any statistical hypotheses and assumptions is derived. The derivation is based on the smoothing of the microscopic dynamic characteristics of a many-body system, taking into account the retardation of the interactions between them. The resulting equation generalizes the classical equation of motion for fluids. Several particular cases of the resulting equation, as well as its connection with the dynamic density functional theory, are considered.