Information geometry and Bose–Einstein condensation

Abstract

It is a long held conjecture in the connection between information geometry (IG) and thermodynamics that the curvature endowed by IG diverges at phase transitions. Recent work on the IG of Bose–Einstein (BE) gases challenged this conjecture by saying that in the limit of fugacity approaching unit—where BE condensation is expected—the curvature does not diverge; rather, it converges to zero. However, as the discontinuous behavior that identifies condensation is only observed at the thermodynamic limit, a study of the IG curvature at a finite number of particles, [Formula: see text], is in order from which the thermodynamic behavior can be observed by taking the thermodynamic limit ([Formula: see text]) posteriorly. This article presents such a study. We find that for a trapped gas, as [Formula: see text] increases, the values of curvature decrease proportionally to a power of [Formula: see text], while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature. This means that, in the thermodynamic limit, the curvature has a limited value where a phase transition is observed, contradicting the forementioned conjecture.