Canonical partition function for anomalous systems described by the $\kappa$-entropy

Abstract

Starting from the $\kappa$-distribution function, obtained by applying the maximal entropy principle to the $\kappa$-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical $\kappa$-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the $\kappa$-partition function. The relationship between the associated $\kappa$-free energy and the $\kappa$-entropy is also discussed.

8 pages, no figures. Work presented at the International conference Complexity and Nonextensivity: New Trends in Statistical Mechanics. - Yukawa Institute for Theoretical Physics - (14-18 March 2005) Kyoto, Japan

Cited by in corpus (14)

• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• Relativistic Entropy and Related Boltzmann Kinetics
• Asymptotic solutions of a nonlinear diffusive equation in the framework of $\kappa$-generalized statistical mechanics
• New power-law tailed distributions emerging in $\kappa$-statistics
• Composition law of $\kappa$-entropy for statistically independent systems
• Physical origin of the power-law tailed statistical distributions
• Relativistic kinetics and power-law tailed distributions
• Relativistic Roots of $\kappa$-Entropy
• A nonlinear drift which leads to $\kappa$-generalized distributions
• Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov-Nagumo average
• Power-Law tailed statistical distributions and Lorentz transformations
• Thermal and mechanical equilibrium among weakly interacting systems in generalized thermostatistics framework
• Nonlinear Kinetics on Lattices based on the Kinetic Interaction Principle