Path Entropy Changes in Adiabatic Approximation

TL;DR

This paper applies the adiabatic theorem to Markovian systems to analyze path entropy changes, distinguishing between adiabatic and diabatic contributions, and clarifies the correct partitioning of entropy terms in such processes.

Contribution

It introduces a new formulation for path entropy changes in adiabatic processes, clarifying the roles of work and heat contributions and correcting previous assumptions about entropy term partitioning.

Findings

Total path entropy change equals adiabatic path entropy change in adiabatic processes.

Adiabatic entropy change is due to work, not heat.

Corrected the partitioning of entropy contributions from previous literature.

Abstract

By applying adiabatic theorem to a Markovian system, we calculate the adiabatic and diabatic entropy changes along a path. As well known, the total path entropy change is separated into two parts, system and environment entropy changes, $\Delta S_{tot} = \Delta S_{sys} + \Delta S_{env}$. The environment entropy change, $\Delta S_{env}$, is divided again into two parts, an adiabatic contribution due to work, $\Delta S_{\mathcal{W}}$, and a diabatic contributions due to heat, $\Delta S_{\mathcal{Q}}$. In an adiabatic process, total path entropy change is same with the adiabatic path entropy change, $\Delta S_{A}$, which is given by sum of system entropy change and adiabatic contribution, $\Delta S_{A} = \Delta S_{sys} + \Delta S_{\mathcal{W}}$. Mathematical form of $\Delta S_{A}$ is a type of excess heat entropy change, but $\Delta S_{A}$ is due to work. By which, it is shown that the terms adiabatic and non-adiabatic contributions of $\Delta S_{na}$ and $\Delta S_{a}$ in [Phys. Rev. Lett. {\bf 104}, 090601 (2010)] should be completely switched, $i.e.$ $\Delta S_{na} \rightarrow \Delta S_{A}$ and $\Delta S_{a} \rightarrow \Delta S_{\mathcal{Q}}$ in fact.