Thermodynamic Irreversibility from high-dimensional Hamiltonian Chaos

TL;DR

This paper introduces a new measure called irreversible information loss to characterize thermodynamic irreversibility in high-dimensional Hamiltonian systems, linking it to the second law and Boltzmann entropy through theoretical proofs and numerical validation.

Contribution

It defines a novel quantity, irreversible information loss, and proves its relation to thermodynamic irreversibility and the second law in complex Hamiltonian systems.

Findings

Irreversible information loss satisfies a second law inequality.

Most probable irreversible information loss equals the change in Boltzmann entropy.

Numerical experiments confirm the theoretical predictions.

Abstract

This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to characterize the thermodynamic irreversibility. It is proved that this new quantity satisfies an inequality associated with the second law of thermodynamics. Based on the assumption that these systems possess the mixing property and certain large deviation properties in the thermodynamic limit, it is argued reasonably that the most probable value of the irreversible information loss is equal to the change of the Boltzmann entropy in statistical mechanics, and that it is always a non-negative value. The consistency of our argument is confirmed by numerical experiments with the aid of the definition of a quantity we refer to as the excess information loss.