Relaxation, the Boltzmann-Jeans Conjecture and Chaos

TL;DR

This paper investigates slow relaxation in a Hamiltonian system, confirming the Boltzmann-Jeans conjecture and linking relaxation time to residual chaos and entropy increase.

Contribution

It demonstrates the exponential relation of relaxation time to excitation energy and introduces residual Kolmogorov-Sinai entropy as a key factor.

Findings

Relaxation time increases exponentially with the square root of excitation energy.

Residual Kolmogorov-Sinai entropy is inversely proportional to relaxation time.

Thermodynamic entropy increase is proportional to residual Kolmogorov-Sinai entropy.

Abstract

Slow (logarithmic) relaxation from a highly excited state is studied in a Hamiltonian system with many degrees of freedom. The relaxation time is shown to increase as the exponential of the square root of the energy of excitation, in agreement with the Boltzmann-Jeans conjecture, while it is found to be inversely proportional to residual Kolmogorov-Sinai entropy, introduced in this Letter. The increase of the thermodynamic entropy through this relaxation process is found to be proportional to this quantity.