Information geometry for the strongly degenerate ideal Bose-Einstein fluid

The thermodynamic geometry of the Bose-Einstein fluid in the framework of information geometry is revisited, and particularly the strongly degenerate case is considered for a finite volume. Therefore, in the construction of the metric, the term related to the number of particles that accumulate in the ground state is taken into account, and we allow to explore its contribution to the curvature in highly quantum conditions, namely for temperature values where the ratio lambda(3)/V (thermal de Broglie wavelength cubed over volume) is greater than unity. It is found that in this regime, the ground state contribution is relevant in the limit of condensation and it strongly affects the behavior of the scalar curvature R. We show, numerically and analytically, that R is finite and smoothly approaches to zero in the limit eta -> 1, namely as the fugacity tends to the numerical value where the condensation occurs the quantum effects are stronger. Consequently, when both phases are taken into account, there exist a region for extremely low temperatures where the curvature is regular, similarly to other quantum phase transitions reported in the literature. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study revisits the thermodynamic geometry of the Bose-Einstein fluid within the framework of information geometry, particularly considering the strongly degenerate case for a finite volume. The ground state contribution is found to be relevant in highly quantum conditions, affecting the scalar curvature R in the limit of condensation. The curvature is shown to be finite and approach zero smoothly as the fugacity tends to the numerical value where condensation occurs, indicating stronger quantum effects.