How isolated is enough for an "isolated" system in statistical mechanics?

TL;DR

This paper investigates how quantum dephasing influences entropy changes during free expansion, revealing classical behavior in large systems and quantum effects in small systems, thus clarifying the origins of irreversibility.

Contribution

It introduces quantum dephasing as a key factor in entropy increase, bridging classical and quantum thermodynamics in free expansion processes.

Findings

Classical entropy increase occurs when system size is much larger than thermal wavelength.

Quantum effects cause deviations from classical predictions in small systems.

Quantum dephasing is essential to understanding irreversibility in thermodynamics.

Abstract

Irreversible processes are frequently adopted to account for the entropy increase in classical thermodynamics. However, the corresponding physical origins are not always clear, e.g. in a free expansion process, a typical model in textbooks. In this letter, we study the entropy change during free expansion for a particle with the thermal de Broglie wavelength ($\lambda_{T}$) in a one-dimensional square trap with size $L$. By solely including quantum dephasing as an irreversible process, we recover classical result of entropy increase in the classical region ($L\gg\lambda_{T}$), while predict prominent discrepancies in the quantum region ($L\ll\lambda_{T}$) because of non-equilibrium feature of trapped atoms after expansion. It is interesting to notice that the dephasing, though absent in classical system, is critical to clarify mysteries in classical thermodynamics.