The role of the number of degrees of freedom and chaos in macroscopic irreversibility

TL;DR

This paper explores how the number of degrees of freedom and chaos influence macroscopic irreversibility, emphasizing that irreversibility arises in large systems regardless of chaos, supported by simple numerical examples.

Contribution

It demonstrates that irreversibility is inherent in large systems with many degrees of freedom and is independent of chaos, challenging common assumptions about chaos's role.

Findings

Irreversibility appears at the single-trajectory level in large systems.

Chaos is not essential for macroscopic irreversibility.

Irreversible behavior is observed in both chaotic and non-chaotic systems.

Abstract

This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by Boltzmann. Emphasis will be put on the fact that, in systems characterized by a very large number of degrees of freedom, irreversibility is already manifest at a single-trajectory level for the vast majority of the far-from-equilibrium initial conditions - a property often referred to as typicality. We also discuss the importance of the interaction among the microscopic constituents of the system and the irrelevance of chaos to irreversibility, showing that the same irreversible behaviours can be observed both in chaotic and non-chaotic systems.