Dissipation in gases trapped in time-dependent external potentials

TL;DR

This paper studies how a gas's energy changes under a time-dependent trap, revealing that relaxation processes can both produce entropy and reduce dissipation by restoring equilibrium.

Contribution

It introduces a model using the Boltzmann equation with relaxation time to analyze dissipation in gases under dynamic potentials, highlighting the dual role of relaxation.

Findings

Relaxation reduces dissipation during potential changes.

Energy with relaxation is always less than the relaxation-less case for small times.

Relaxation processes produce entropy but also help restore equilibrium.

Abstract

We investigate an ideal gas in a time--dependent external trapping potential. We use the Boltzmann equation with the relaxation time ansatz to explore the time--dependent energy of an adiabatically isolated system. In particular we are interested on the dissipation during a potential change along a given protocol with finite velocity. The role of the relaxation less evolution as a limiting case is studied: starting from an equilibrium distribution and for small times the energy of the gas with relaxation is always smaller than that of the relaxation--less. This means that relaxation processes show an ambivalent behavior: on the one hand entropy production, but on the other hand reduction of dissipation by driving back the system into equilibrium.