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Thermostatistics of a Relativistic Gas : Equilibrium and Non-equilibrium Properties

The introduction of models to simulate dynamics of relativistic gaseous systems is among the latest efforts made in the recent decades to investigate the relativistic generalizations of statistical thermodynamics. Relativistic thermodynamics was born in the early 20th century to investigate the consequences of Einstien’s special relativity on thermodynamic systems. A simple and important question is the Lorentz transformation property of temperature. Other questions are related to relativistic generalization of equilibrium statistical mechanics. For example, Maxwell-Boltzmann (MB) distribution, the corner stone of classical statistical mechanics, permits velocities greater than the speed of light, v > c, in direct conflict with a basic assumption of special relativity. The resolution of such issues has been long in the coming and marred with much controversies. In no more than half a century, thermodynamic approach led to such a confusing atmosphere in which one could not decide whether a moving body appears cooler, hotter or at the same temperature. Followers of the statistical approach also put multiple generalizations of MB distribution on the table, notably Jüttner and modified Jüttner function each with its own merits. One reason for the ongoing discussion is the difficulty of treating manyparticle interactions in a relativistically consistent manner. Another reason is the lack of experimental evidences to verify the validity of proposed theories in this field. Therefore, it seems that the only solution is to present simple and realistic models to simulate relativistic systems. This, however is not an easy task, because the microscopic dynamics of such particle systems presents many difficulties. Some of the difficulties include: the choice of the reference frame, since every particle has a different proper time; the form of the interaction potential, since the action and reaction principle holds only