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Entropy 2017, 19(9), 436;

From Relativistic Mechanics towards Relativistic Statistical Mechanics

Retired Research Director of Sezione INFN di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy
Received: 22 May 2017 / Revised: 26 July 2017 / Accepted: 5 August 2017 / Published: 23 August 2017
(This article belongs to the Special Issue Advances in Relativistic Statistical Mechanics)
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Till now, kinetic theory and statistical mechanics of either free or interacting point particles were well defined only in non-relativistic inertial frames in the absence of the long-range inertial forces present in accelerated frames. As shown in the introductory review at the relativistic level, only a relativistic kinetic theory of “world-lines” in inertial frames was known till recently due to the problem of the elimination of the relative times. The recent Wigner-covariant formulation of relativistic classical and quantum mechanics of point particles required by the theory of relativistic bound states, with the elimination of the problem of relative times and with a clarification of the notion of the relativistic center of mass, allows one to give a definition of the distribution function of the relativistic micro-canonical ensemble in terms of the generators of the Poincaré algebra of a system of interacting particles both in inertial and in non-inertial rest frames. The non-relativistic limit allows one to get the ensemble in non-relativistic non-inertial frames. Assuming the existence of a relativistic Gibbs ensemble, also a “Lorentz-scalar micro-canonical temperature” can be defined. If the forces between the particles are short range in inertial frames, the notion of equilibrium can be extended from them to the non-inertial rest frames, and it is possible to go to the thermodynamic limit and to define a relativistic canonical temperature and a relativistic canonical ensemble. Finally, assuming that a Lorentz-scalar one-particle distribution function can be defined with a statistical average, an indication is given of which are the difficulties in solving the open problem of deriving the relativistic Boltzmann equation with the same methodology used in the non-relativistic case instead of postulating it as is usually done. There are also some comments on how it would be possible to have a hydrodynamical description of the relativistic kinetic theory of an isolated fluid in local equilibrium by means of an effective relativistic dissipative fluid described in the Wigner-covariant framework. View Full-Text
Keywords: special relativity; statistical mechanics; kinetic theory special relativity; statistical mechanics; kinetic theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Lusanna, L. From Relativistic Mechanics towards Relativistic Statistical Mechanics. Entropy 2017, 19, 436.

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