Irreversibility, Molecular Chaos, and A Simple Proof of the Second Law

TL;DR

This paper presents a simple proof that entropy in a constant-energy system cannot decrease over time, challenging the common belief that irreversibility solely results from molecular chaos.

Contribution

It provides a novel proof linking irreversibility to probabilistic evolution without relying exclusively on molecular chaos assumptions.

Findings

Entropy cannot decrease at constant energy

Irreversibility is rooted in probabilistic evolution

Molecular chaos is not the only cause of irreversibility

Abstract

The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each microstate probability vanishes only as time diverges, we prove that the entropy of a system at constant energy cannot decrease with time.