Thermodynamics of a bouncer model: a simplified one-dimensional gas

TL;DR

This paper analyzes the dynamical behavior of particles in a one-dimensional bouncer model under gravity, focusing on their approach to steady state with different initial energies and deriving relations for key thermodynamic observables.

Contribution

It provides a detailed description of the evolution to steady state in a dissipative bouncer model, including decay laws and relations for temperature and entropy.

Findings

Exponential decay for large initial energy

Power law decay for low initial energy

Relations between collisions, time, and thermodynamic observables

Abstract

Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative dynamics with inelastic collisions: (i) for large initial energy; (ii) for low initial energy. For (i) we prove an exponential decay while for (ii) a power law marked by a changeover to the steady state is observed. A relation for collisions and time is obtained and allows us to write relevant observables as temperature and entropy as function of either number of collisions and time.