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      Statistical mechanics in the context of special relativity

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          Abstract

          In the present effort we show that \(S_{\kappa}=-k_B \int d^3p (n^{1+\kappa}-n^{1-\kappa})/(2\kappa)\) is the unique existing entropy obtained by a continuous deformation of the Shannon-Boltzmann entropy \(S_0=-k_B \int d^3p n \ln n\) and preserving unaltered its fundamental properties of concavity, additivity and extensivity. Subsequently, we explain the origin of the deformation mechanism introduced by \(\kappa\) and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter \(\kappa\) which results to depend on the light speed \(c\) and reduces to zero as \(c \to \infty\) recovering in this way the ordinary statistical mechanics and thermodynamics. The novel statistical mechanics constructed starting from the above entropy, preserves unaltered the mathematical and epistemological structure of the ordinary statistical mechanics and is suitable to describe a very large class of experimentally observed phenomena in low and high energy physics and in natural, economic and social sciences. Finally, in order to test the correctness and predictability of the theory, as working example we consider the cosmic rays spectrum, which spans 13 decades in energy and 33 decades in flux, finding a high quality agreement between our predictions and observed data. PACS number(s): 05.20.-y, 51.10.+y, 03.30.+p, 02.20.-a

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          Author and article information

          Journal
          21 October 2002
          2002-11-28
          Article
          10.1103/PhysRevE.66.056125
          cond-mat/0210467
          1b84e8a8-9999-4341-95c6-53ee170b9fd3
          History
          Custom metadata
          Phys. Rev. E 66, 056125 (2002)
          17 pages (two columns), 5 figures, RevTeX4, minor typing corrections
          cond-mat.stat-mech cond-mat.soft

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