Mittag-Leffler Quantum Statistics and Thermodynamic Anomalies

Abstract

Building upon the framework established in our recent work [M. Seifi et al., Phys. Rev. E 111, 054114 (2025)], wherein a generalized Maxwell Boltzmann distribution was formulated using the Mittag Leffler function within the superstatistical formalism, we extend this approach to the quantum domain. Specifically, we introduce two statistical distributions,termed the Mittag Leffler Bose Einstein (MLBE) and Mittag Leffler Fermi Dirac (MLFD) distributions, constructed by generalizing the conventional Bose-Einstein and Fermi-Dirac distributions through the Mittag-Leffler function. This generalization incorporates a deformation parameter (α), which facilitates a continuous interpolation between bosonic and fermionic statistics, while inherently capturing nonequilibrium effects and generalized thermodynamic behavior. We analyze the thermodynamic geometry associated with these distributions and identify significant departures from standard statistical models. Notably, the MLBE distribution manifests a Bose-Einstein-like condensation even in the absence of interactions, whereas the MLFD distribution exhibits unconventional features, such as negative heat capacity in the low-temperature regime. These findings highlight the pivotal role of statistical deformation in determining emergent macroscopic thermodynamic phenomena.

15 pages, 10 figures

References in corpus (21)

• Superstatistics
• Non Linear Kinetics underlying Generalized Statistics
• Negative heat capacity in the critical region of nuclear fragmentation: an experimental evidence of the liquid-gas phase transition
• On Generalized Fractional Kinetic Equations
• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Why the Mittag-Leffler function can be considered the Queen function of the Fractional Calculus?
• Thermodynamical features of multifragmentation in peripheral Au + Au Collisions at 35 A.MeV
• Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions
• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
• Scaling Laws of Passive-Scalar Diffusion in the Interstellar Medium
• Thermodynamic Geometry of Fractional Statistics
• Nonperturbative Thermodynamic Geometry of Anyon Gas
• Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics
• New power-law tailed distributions emerging in $\kappa$-statistics
• Condensation of an ideal gas with intermediate statistics on the horizon
• Rotational random walk of the harmonic three body system
• Condensation of an ideal gas obeying non-Abelian statistic
• Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics
• Perturbative Thermodynamic Geometry of Nonextensive Ideal Classical, Bose and Fermi Gases
• Mittag-Leffler functions in superstatistics
• Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution