An anomalous particle-exchange mechanism for two isolated Bose gases merged into one

TL;DR

This paper investigates an anomalous particle-exchange mechanism in merged Bose gases, revealing a decrease in entropy due to effective particle exchange in excited states, challenging conventional thermodynamic expectations.

Contribution

It introduces a novel particle-exchange mechanism explaining entropy decrease in merged Bose gases, supported by numerical evidence and theoretical analysis.

Findings

Entropy decreases upon merging two Bose gases.

Anomalous particle exchange occurs in excited states.

Numerical simulations support the entropy reduction.

Abstract

In an isolated ideal Bose system with a fixed energy, the number of microstates depends solely on the configurations of bosons in excited states, implying zero entropy for particles in the ground state. When two such systems merge, the resulting entropy is less than the sum of the individual entropies. This entropy decrease is numerically shown to arise from an effectively but anomalous exchange of particles in excited states, where $\overline{N}!/(\overline{N}_{1}!\overline{N}_{2}!)<1$. Here, $\overline{N}$, $\overline{N}_{1}$, and $\overline{N}_{2}$ are real decimals representing, respectively, the mean number of particles in excited states in the merged system and the two individual systems before merging, with $\overline{N}<\overline{N}_{1}+\overline{N}_{2}$.