Mittag-Leffler quantum statistics and thermodynamic anomalies

Area of Science:

• Statistical Mechanics
• Quantum Statistics
• Thermodynamics

Background:

• Superstatistics and generalized Maxwell-Boltzmann distributions were previously formulated using the Mittag-Leffler function.
• Conventional Bose-Einstein and Fermi-Dirac statistics describe quantum systems at equilibrium.

Purpose of the Study:

• To extend superstatistical formalism to the quantum domain by generalizing Bose-Einstein and Fermi-Dirac distributions.
• To introduce and analyze the properties of the novel Mittag-Leffler-Bose-Einstein (MLBE) and Mittag-Leffler-Fermi-Dirac (MLFD) distributions.
• To investigate the role of statistical deformation in emergent thermodynamic phenomena.

Main Methods:

• Generalization of Bose-Einstein and Fermi-Dirac distributions using the Mittag-Leffler function.
• Inclusion of a deformation parameter (α) for continuous interpolation between bosonic and fermionic statistics.
• Analysis of thermodynamic geometry and emergent phenomena.

Main Results:

• The MLBE distribution exhibits Bose-Einstein-like condensation without interactions.
• The MLFD distribution displays unconventional features, including negative heat capacity at low temperatures.
• Significant departures from standard statistical models were identified.

Conclusions:

• The developed MLBE and MLFD distributions offer a generalized framework for quantum statistics.
• Statistical deformation plays a crucial role in determining macroscopic thermodynamic behavior.
• These novel distributions capture nonequilibrium effects and generalized thermodynamic properties.