Mutual information and Bose-Einstein condensation

TL;DR

This paper investigates how mutual information behaves in a bosonic quantum field system at finite temperature and chemical potential, revealing a discontinuity at the Bose-Einstein condensation critical temperature.

Contribution

It derives the mutual information for a bosonic system with a specific spatial partition, including effects of Bose-Einstein condensation and chemical potential.

Findings

Mutual information is derived for the system with a specific partition.

The thermal derivative of mutual information shows a finite discontinuity at the critical temperature.

Bose-Einstein condensation influences the behavior of mutual information.

Abstract

In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the geometric entropy corresponding to the specific partition and then we substract its extensive part which coincides with the thermal entropy of the system. In the case of non-zero chemical potential, we examine the influence of the underlying Bose-Einstein condensation on the behavior of the mutual information, and we find that its thermal derivative possesses a finite discontinuity at exactly the critical temperature.