Towards a relativistic statistical theory

Abstract

In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we show that the special relativity imposes a proper one parameter continuous deformation also to the expression of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits to construct a coherent and selfconsistent relativistic statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002); Phys. Rev. E {\bf 72}, 036108 (2005)], preserving the main features (maximum entropy principle, thermodynamic stability, Lesche stability, continuity, symmetry, expansivity, decisivity, etc.) of the classical statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence.

Physica A (2006). Proof corrections

References in corpus (8)

• Statistical mechanics in the context of special relativity
• Non Linear Kinetics underlying Generalized Statistics
• Statistical mechanics in the context of special relativity II
• Deformed exponentials and logarithms in generalized thermostatistics
• Generalized thermodynamics and kinetic equations: Boltzmann, Landau, Kramers and Smoluchowski
• Generalized thermostatistics based on deformed exponential and logarithmic functions
• Maximum Renyi entropy principle for systems with power--law Hamiltonian
• Generalized entropy optimized by an arbitrary distribution

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• Relativistic Roots of $\kappa$-Entropy
• Unifying Aspects of Generalized Calculus
• Stationarity, soft ergodicity, and entropy in relativistic systems
• Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data
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