Emergent pseudo time-irreversibility in the classical many-body system of pair interacting particles

TL;DR

This paper investigates how macroscopic pseudo time-irreversibility emerges in classical many-body systems of interacting particles, deriving continuum equations without statistical mechanics and providing numerical evidence for irreversible thermal and momentum transport.

Contribution

It introduces a novel derivation of continuum equations directly from Hamiltonian dynamics and demonstrates the emergence of pseudo time-irreversibility in such systems.

Findings

Numerical evidence of pseudo-irreversible thermal equilibration

Observation of heat and momentum transport consistent with irreversibility

Discussion of non-diffusional relaxation mechanisms

Abstract

In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in the closed classical many-body system of pair interacting particles. First, exact continuum equations are derived to the Hamiltonian dynamics without the utilisation of statistical mechanics. Next, it is shown that the momentum density field incorporates the thermal degrees of freedom in the considered scaling limit, and therefore initial condition indicated pseudo time-irreversible solutions may exist to the dynamical equations. Numerical evidence for pseudo-irreversible thermal equilibration, heat and momentum transport is provided. Finally, the possible reasons of the numerically obtained non-diffusional relaxation of macroscopic order is discussed.