Relativistic transformation of the canonical distribution function in relativistic statistical mechanics

Relativistic Statistical Mechanics vs. Relativistic Thermodynamics

“…On the other hand, it has to be noticed that even if Balescu [6] has committed the mistake of considering the invariance of the regular relativistic thermodynamics [12,13,18], his proposal for a Relativistic Statistical Mechanics is correct under the assumption that the Thermodynamics deduced from it is the RRT. In order to explicitly shows this aspect, this connection has to be done by using the covariant representation of the RRT.…”

“…Moreover, since the regular concept of internal energy has to be abandoned and substituted by a redefined energy, it is possible to obtain the invariance of the form of Thermodynamics. Starting by using the Redefined Relativistic Thermodynamics [RRT] an incipient non-covariant statistical theory has been developed by López-Carrera and Ares de Parga [13]. On the other hand, Nakamura [14] has proposed a variation to the van-Kampen theory [15] modified by Israel [16,17] which correct the tensor character of it.…”

“…As we will see later in the paper, the Rohrlich-Gamba proposal is another one and it possesses many similitudes with the ideas of Ott, Möller and Requardt. By using the RRT and a statistical theory developed by López-Carrera and Ares de Parga [13] based on the Balescu Statistical Mechanics theory [6,12,13], they [13] have obtained the relativistic Js of an ideal gas. Nevertheless, the result is based on a non-covariant theory.…”

A further analysis of the energy-momentum for a system of point particles and for a perfect fluid in finite volume

“…(99). This theory has been used to analyze the black body radiation from a moving frame [27], [28], to solve the Thermodynamics of the mixture of two black bodies [30] including the conservation of the heat in any reference frame, to propose a relativistic thermometer [30] [31], to obtain a Statistical Relativistic Mechanics [32], to deduce the Jüttner distribution [32] and finally to show the invariance of the equations of states [33].…”

“…Nevertheless, in the first years of this century, Landsberg and Matsas proposed that it is not possible to define a universal definition of the temperature [6], [19], [20] [21], [22]. Based on Fermi ideas of instantaneity and a formal definition of a 4−vector [23], [24], [25], [26], Ares de Parga et al developed a new theory which is known as the Redefined Relativistic Thermodynamics [27], [28], [29], [30], [31], [32], [33], [34].…”