Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution

Abstract

The thermodynamic parameter space is flat for an ideal classical gas with non-interacting particles. In contrast, for an ideal quantum Bose (Fermi) gas, the thermodynamic curvature is positive (negative), indicating intrinsic attractive (repulsive) interactions. We generalize the classical Maxwell-Boltzmann distribution by employing a generalized form of the exponential function, proposing the Mittag-Leffler Maxwell-Boltzmann distribution within the framework of superstatistics. We demonstrate that the generalization parameter, $\alpha$, quantifies the statistical interaction. When $\alpha =1$, the distribution coincides with the standard classical Maxwell-Boltzmann distribution, where no statistical interaction is present. For $0<\alpha <1$ ($\alpha >1$), the statistical interaction is repulsive (attractive), corresponding to a negative (positive) thermodynamic curvature of the system.

12 pages,11 figures

References in corpus (31)

• Anyons in an exactly solved model and beyond
• Magnetic Monopoles in Spin Ice
• Charged AdS Black Holes and Catastrophic Holography
• Quantum Criticality in Heavy Fermion Metals
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Superstatistics
• Non Linear Kinetics underlying Generalized Statistics
• Non Fermi-Liquid States and Pairing of a general Model of Copper-Oxide Metals
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Fractional statistics in anyon collisions
• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Critical Behavior in the Rotating D-branes
• Probabilities and Path-Integral Realization of Exclusion Statistics
• Quantum critical lines in holographic phases with (un)broken symmetry
• Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions
• Haldane exclusion statistics and second virial coefficient
• Thermodynamic Geometry of Deformed Bosons and Fermions
• 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
• Comments on the Properties of Mittag-Leffler Function
• Condensation of an ideal gas with intermediate statistics on the horizon
• Rotational random walk of the harmonic three body system
• Two temperature Ising Model
• 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
• Scalar curvature of systems with fractal distribution functions

Cited by in corpus (1)

• Mittag-Leffler Quantum Statistics and Thermodynamic Anomalies