Information geometry and Bose-Einstein condensation
- URL: http://arxiv.org/abs/2302.03182v1
- Date: Tue, 7 Feb 2023 01:22:39 GMT
- Title: Information geometry and Bose-Einstein condensation
- Authors: Pedro Pessoa
- Abstract summary: 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 -- curvature does not diverge, rather it converges to zero.
We find that for a trapped gas, as $N$ increases, the values of curvature decrease proportionally to a power of $N$ while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 -- curvature does not diverge, rather it converges to
zero. However, as the discontinuous behavior that identify condensation is only
observed at the thermodynamic limit, a study of IG curvature at finite number
of particles, $N$, is in order from which the thermodynamic behaviour can be
observed by taking the thermodynamic limit ($N\to \infty$) posteriorly. This
article presents such study, which was made possible by the recent advances
presented in [Phys. Rev. A 104, 043318 (2021)]. We find that for a trapped gas,
as $N$ increases, the values of curvature decrease proportionally to a power of
$N$ while the temperature at which the maximum value of curvature occurs
approaches the usually defined critical temperature. This means that, in the
thermodynamic limit, curvature has a limited value where a phase transition is
observed, contradicting the forementioned conjecture.
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