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Information geometry for the strongly degenerate ideal Bose–Einstein fluid

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  • López-Picón, J.L.
  • López-Vega, J. Manuel

Abstract

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 λ3∕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 η→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.

Suggested Citation

  • López-Picón, J.L. & López-Vega, J. Manuel, 2021. "Information geometry for the strongly degenerate ideal Bose–Einstein fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    • Handle: RePEc:eee:phsmap:v:580:y:2021:i:c:s0378437121004179
    DOI: 10.1016/j.physa.2021.126144
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    References listed on IDEAS

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    1. Dey, Anshuman & Roy, Pratim & Sarkar, Tapobrata, 2013. "Information geometry, phase transitions, and the Widom line: Magnetic and liquid systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6341-6352.
    2. Ghikas, Demetris P.K. & Oikonomou, Fotios D., 2018. "Towards an information geometric characterization/classification of complex systems. II. Critical parameter values from the (c,d)-manifold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 365-374.
    3. Ghikas, Demetris P.K. & Oikonomou, Fotios D., 2018. "Towards an information geometric characterization/classification of complex systems. I. Use of generalized entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 384-398.
    4. Janke, W. & Johnston, D.A. & Kenna, R., 2004. "Information geometry and phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 181-186.
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