Information geometry for FermiDirac and BoseEinstein quantum statistics
Abstract
Information geometry is an emergent branch of probability theory that consists of assigning a Riemannian differential geometry structure to the space of probability distributions. We present an information geometric investigation of gases following the FermiDirac and the BoseEinstein quantum statistics. For each quantum gas, we study the information geometry of the curved statistical manifolds associated with the grand canonical ensemble. The FisherRao information metric and the scalar curvature are computed for both fermionic and bosonic models of noninteracting particles. In particular, by taking into account the ground state of the ideal bosonic gas in our information geometric analysis, we find that the singular behavior of the scalar curvature in the condensation region disappears. This is a counterexample to a long held conjecture that curvature always diverges in phase transitions.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 August 2021
 DOI:
 10.1016/j.physa.2021.126061
 arXiv:
 arXiv:2103.00935
 Bibcode:
 2021PhyA..57626061P
 Keywords:

 Information geometry;
 BoseEinstein condensates;
 Fermi gases;
 Information theory;
 Quantum Physics;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Physica A 576, 126061 (2021)