# Macroscopic irreversibility and decay to kinetic equilibrium of the 1-body PDF for finite hard-sphere systems

## TL;DR

This paper investigates the conditions under which macroscopic irreversibility and decay to equilibrium occur in finite hard-sphere systems, using an axiomatic statistical mechanics framework and the Master kinetic equation.

## Contribution

It introduces the concept of Master kinetic information and proves that irreversibility and decay to equilibrium are realized under certain smooth solutions of the Master kinetic equation.

## Key findings

- Macroscopic irreversibility is characterized within the axiomatic framework.
- Decay to kinetic equilibrium is demonstrated for suitable solutions.
- The Master kinetic information functional is key to these properties.

## Abstract

The conditions for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the 1-body probability density function (PDF) associated with hard-sphere systems are investigated. The problem is set in the framework of the axiomatic "ab initio" theory of classical statistical mechanics developed recently and the related establishment of an exact kinetic equation realized by the Master equation for the same kinetic PDF. As shown in the paper the task involves the introduction of a suitable functional of the 1-body PDF, identified here with the Master kinetic information. It is then proved that, provided the same PDF is prescribed in terms of suitably-smooth, i.e., stochastic, solution of the Master kinetic equation, the two properties indicated above are indeed realized.