Kinetical Foundations of Non Conventional Statistics

Abstract

After considering the kinetical interaction principle (KIP) introduced in ref. Physica A {\bf296}, 405 (2001), we study in the Boltzmann picture, the evolution equation and the H-theorem for non extensive systems. The $q$-kinetics and the $\kappa$-kinetics are studied in detail starting from the most general non linear Boltzmann equation compatible with the KIP.

11 pages, no figures. Contribution paper to the proseedings of the International School and Workshop on Nonextensive Thermodynamics and Physical Applications, NEXT 2001, 23-30 May 2001, Cagliari Sardinia, Italy (Physica A)

References in corpus (3)

• Non Linear Kinetics underlying Generalized Statistics
• Nonextensive Thermostatistics and the H-Theorem
• H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics

Cited by in corpus (26)

• Anomalous Diffusion in View of Einstein's 1905 Theory of Brownian Motion
• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Probing the cosmological viability of non-gaussian statistics
• Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law
• Power-law statistics and stellar rotational velocities in the Pleiades
• Basic-deformed thermostatistics
• Jeans instability criterion from the viewpoint of non-gaussian statistics
• Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology
• Entropic Forms and Related Algebras
• $P-v$ criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics
• Statistical approaches on the apparent horizon entropy and the generalized second law of thermodynamics
• Tsallis and Kaniadakis statistics from the viewpoint of entropic gravity formalism
• The $H$-theorem in $\kappa$-statistics: influence on the molecular chaos hypothesis
• Loop Quantum Gravity Immirzi parameter and the Kaniadakis statistics
• Interacting particles system revisited in the framework of the q-deformed algebra
• Composition law of $\kappa$-entropy for statistically independent systems
• The kappa parameter and kappa-distribution in kappa-deformed statistics for the systems in an external field
• Conservative Force Fields in Non-Gaussian Statistics
• k-Deformed Fourier Transform
• Physical origin of the power-law tailed statistical distributions
• Relativistic Roots of $\kappa$-Entropy
• Statistical approaches and the Bekenstein bound conjecture in Schwarzschild black holes
• Non-Gaussian thermostatistical considerations upon the Saha equation
• Entropic Gravity and Cosmology in Kaniadakis Statistics
• Nonlinear Kinetics on Lattices based on the Kinetic Interaction Principle
• Derivation of a statistical model for classical systems obeying fractional exclusion principle