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Towards a relativistic statistical theory

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  • Kaniadakis, G.

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 [G. Kaniadakis, Phys. Rev. E 66 (2002) 056125; G. Kaniadakis, Phys. Rev. E 72 (2005) 036108], 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.

Suggested Citation

  • Kaniadakis, G., 2006. "Towards a relativistic statistical theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 17-23.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:17-23
    DOI: 10.1016/j.physa.2006.01.016
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    Cited by:

    1. McKeague, Ian W., 2015. "Central limit theorems under special relativity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 149-155.
    2. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Eck, Daniel J. & McKeague, Ian W., 2016. "Central Limit Theorems under additive deformations," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 156-162.

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