Thermodynamics of a time dependent and dissipative oval billiard: a heat transfer and billiard approach

TL;DR

This paper investigates the statistical behavior of particle velocities in a time-dependent, dissipative oval billiard, analyzing steady-state temperature using heat transfer principles and billiard dynamics through simulations and theory.

Contribution

It introduces a combined approach using heat transfer laws and billiard dynamics to analyze dissipative, time-dependent billiards, providing new insights into their steady-state behavior.

Findings

Average squared velocity reaches a steady state.

Steady state can be described by heat transfer and billiard dynamics.

Numerical simulations support theoretical predictions.

Abstract

We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the particles with the boundary of the billiard are inelastic leading the average squared velocity to reach a steady state dynamics for large enough time. The description of the stationary state is made by using two different approaches: (i) heat transfer motivated by the Fourier law and, (ii) billiard dynamics using either numerical simulations and theoretical description.