A Novel Trick to Overcome the Phase Space Volume Change and the Use of Hamiltonian Trajectories with an emphasis on the Free Expansion

TL;DR

This paper introduces a new method to apply Hamiltonian trajectories to nonequilibrium thermodynamics during free expansion, overcoming phase space volume change issues, and clarifies the nature of microwork in isolated systems.

Contribution

It proposes a novel trick to handle phase space volume changes in Hamiltonian trajectories during free expansion, ensuring thermodynamic consistency and aiding simulations.

Findings

Microwork done by microstates is the dissipated work in free expansion.

The microwork is nonnegative in free expansion processes.

The proposed method is thermodynamically consistent and useful for simulations.

Abstract

We extend and successfully apply a recently proposed microstate nonequilibrium thermodynamics to study expansion/contraction processes. Here, the numbers of initial and final microstates are different so they cannot be connected by unique Hamiltonian trajectories. This commonly happens when the phase space volume changes, and has not been studied so far using Hamiltonian trajectories that can be inverted to yield an identity mapping between initial and final microstates as the parameter in the Hamiltonian is changed. We propose a trick to overcome this hurdle with a focus on free expansion in an isolated system, where the concept of dissipated work is not clear. The trick is shown to be thermodynamically consistent and can be extremely useful in simulation. We justify that it is the thermodynamic average of the internal microwork done by a microstate that is dissipated; this microwork is different from the exchange microwork with the vacuum, which vanishes. We also establish that the microwork is nonnegative for free expansion, which is remarkable, since its sign is not fixed in a general process.