Work done on a single-particle gas during an adiabatic compression/expansion process

TL;DR

This paper analytically investigates the work done on a single-particle gas during adiabatic compression and expansion, highlighting the role of ergodicity breaking and initial conditions in irreversibility and energy transfer.

Contribution

It provides an analytical relation between piston collisions and position, and explores how initial distributions affect net energy transfer in adiabatic processes.

Findings

Derived an explicit formula for piston-particle collisions.

Identified ergodicity breaking as a source of irreversibility.

Showed initial distributions can prevent net energy transfer.

Abstract

We compute the average work done by an external agent, driving a piston at constant speed, over a single particle gas going through an adiabatic compression and expansion process. To do so, we get the analytical expression relating the number of collisions between the piston and the particle with the position of the piston during the process. The ergodicity breaking of the system during the process is identified as the source of its irreversibility. In addition, we observe that by using particular initial distributions for the state of the particle, it is possible to preclude the possibility of a net energy transfer from the agent to the particle during the process.