A geometrothermodynamic approach to ideal quantum gases and Bose-Einstein condensates
Year: 2015
Type: preprint
Abstract: We analyze in the context of geometrothermodynamics the behavior of ideal quantum gases which satisfy either the Fermi statistics or the Bose statistics. Although the corresponding Hamiltonian does not contain a potential, indicating the lack of classical thermodynamic interaction, we show that the curvature of the equilibrium space is non-zero, and can be interpreted as a measure of the effective quantum interaction between the gas particles. In the limiting case of a classical Boltzmann gas, we show that the equilibrium space becomes flat, as expected from the physical viewpoint. In addition, we derive a thermodynamic fundamental equation for the Bose-Einstein condensation and, using the Ehrenfest scheme, we show that it can be considered as a first order phase transition which in the equilibrium space corresponds to a curvature singularity. This result indicates that the curvature of the equilibrium space can be used to measure the thermodynamic interaction in classical and quantum systems.
Source: arXiv (Cornell University)
Authors: Hernando Quevedo, Sasha A. Zaldivar
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2279627196