Nonequilibrium Systems : Hard Disks and Harmonic Oscillators Near and Far From Equilibrium

TL;DR

This paper explores how advances in dynamical systems theory, including chaos and fractal analysis, enhance understanding of nonequilibrium statistical mechanics through computer simulations of small deterministic systems.

Contribution

It connects dynamical systems concepts like Lyapunov instability and fractal distributions to thermodynamic irreversibility in nonequilibrium systems.

Findings

Chaos in small systems explains equilibration processes

Fractal distributions characterize nonequilibrium states

Lyapunov instability relates to thermodynamic irreversibility

Abstract

We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and four-dimensional phase spaces. These models provide us with a basis for understanding equilibration and thermodynamic irreversibility in terms of Lyapunov instability, fractal distributions, and thermal constraints