Relativistic Roots of $\kappa$-Entropy

Abstract

The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin--Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the $\kappa$-entropy and its special limiting case, the classical Boltzmann--Gibbs--Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from $\kappa$-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the $\kappa$-formalism, which emerges from the $\kappa$-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on $\kappa$-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the $\kappa$-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized.

References in corpus (72)

• Statistical mechanics in the context of special relativity
• Non Linear Kinetics underlying Generalized Statistics
• Statistical mechanics in the context of special relativity II
• H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics
• Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics
• Kaniadakis holographic dark energy and cosmology
• Deformed exponentials and logarithms in generalized thermostatistics
• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• A new one parameter deformation of the exponential function
• Group entropies, correlation laws and zeta functions
• k-Generalized Statistics in Personal Income Distribution
• The k-generalized distribution: A new descriptive model for the size distribution of incomes
• Deformed logarithms and entropies
• Non-gaussian statistics and stellar rotational velocities of main sequence field stars
• Kappa-deformed Statistics and the Formation of a Quark-Gluon Plasma
• Generalized Kinetic Equations for a System of Interacting Atoms and Photons: Theory and Simulations
• Two generalizations of the Boltzmann equation
• Relativistic Entropy and Related Boltzmann Kinetics
• Kinetical Foundations of Non Conventional Statistics
• Stabilities of generalized entropies
• Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law
• A two-parameter generalization of Shannon-Khinchin Axioms and the uniqueness theorem
• Power-law statistics and stellar rotational velocities in the Pleiades
• A generalized statistical model for the size distribution of wealth
• Jeans instability criterion from the viewpoint of non-gaussian statistics
• Lesche Stability of $\kappa$-Entropy
• $\kappa$-exponential models from the geometrical viewpoint
• $\kappa$-generalization of Gauss' law of error
• Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology
• The property of kappa-deformed statistics for a relativistic gas in an electromagnetic field: kappa parameter and kappa-distribution
• Entropic Forms and Related Algebras
• $P-v$ criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics
• Towards a relativistic statistical theory
• The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis
• Corrections to Friedmann equations inspired by Kaniadakis entropy
• Tsallis and Kaniadakis statistics from the viewpoint of entropic gravity formalism
• Asymptotic solutions of a nonlinear diffusive equation in the framework of $\kappa$-generalized statistical mechanics
• The $H$-theorem in $\kappa$-statistics: influence on the molecular chaos hypothesis
• Canonical partition function for anomalous systems described by the $\kappa$-entropy
• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• Loop Quantum Gravity Immirzi parameter and the Kaniadakis statistics
• A k-generalized statistical mechanics approach to income analysis
• Exploiting the flexibility of a family of models for taxation and redistribution
• New power-law tailed distributions emerging in $\kappa$-statistics
• Kaniadakis holographic dark energy in Brans-Dicke cosmology
• Multifractal spectrum of phase space related to generalized thermostatistics
• Nonextensive random-matrix theory based on Kaniadakis entropy
• Holographic dark energy through Kaniadakis entropy in non flat universe
• The kappa parameter and kappa-distribution in kappa-deformed statistics for the systems in an external field
• Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems
• An overview of generalized entropic forms
• Non-gaussian statistics and the relativistic nuclear equation of state
• Statistical descriptions of nonlinear systems at the onset of chaos
• Conservative Force Fields in Non-Gaussian Statistics
• Bose-Einstein Condensation in the Framework of $\kappa$-Statistics
• Thermodynamic stability conditions for nonadditive composable entropies
• Entropy production and Pesin-like identity at the onset of chaos
• Physical origin of the power-law tailed statistical distributions
• Sensitivity function and entropy increase rates for z-logistic map family at the edge of chaos
• Nonextensive and superstatistical generalizations of random-matrix theory
• Relativistic kinetics and power-law tailed distributions
• A nonlinear drift which leads to $\kappa$-generalized distributions
• Statistical field theories deformed within different calculi
• Gamow Temperature in Tsallis and Kaniadakis Statistics
• Power-Law tailed statistical distributions and Lorentz transformations
• Kappa-deformed random-matrix theory based on Kaniadakis statistics
• On the Kaniadakis distributions applied in statistical physics and natural sciences
• The two parameters (k, r) in the generalized statistics
• Kaniadakis entropy-based characterization of IceCube PeV neutrino signals
• Entropic Gravity and Cosmology in Kaniadakis Statistics
• Black branes in asymptotically Lifshitz spacetimes in $\kappa$-deformed Horndeski gravity

Cited by in corpus (1)

• A unified framework for divergences, free energies, and Fokker-Planck equations