Computation of entropy increase for Lorentz gas and hard disks

TL;DR

This paper calculates entropy changes in Lorentz gas and hard disk systems, revealing exponential growth during initial relaxation and linking entropy increase rates to Lyapunov exponents.

Contribution

It introduces a method to compute entropy functionals for non-stationary particle distributions in Lorentz gas and hard disks, highlighting the role of particle beams and Lyapunov exponents.

Findings

Entropy increases exponentially during initial relaxation.

Particle beams have the highest entropy and entropy increase.

Entropy growth rate is bounded by sums of positive Lyapunov exponents.

Abstract

Entropy functionals are computed for non-stationary distributions of particles of Lorentz gas and hard disks. The distributions consisting of beams of particles are found to have the largest amount of entropy and entropy increase. The computations show exponentially monotonic increase during initial time of rapid approach to equilibrium. The rate of entropy increase is bounded by sums of positive Lyapounov exponents.