Abstract
A full and consecutive analysis of the dynamic and thermodynamic properties of an ideal gas of relativistic particles with Lorentz–Einstein dispersion law and arbitrary number of translational degrees of freedom is carried out. Gibbs statistical mechanics is used along with Bogolyubov’s concept of quasiaverages and the generalized version of the Bogolyubov–Zubarev theorem in the classical regime well beyond the temperature of the quantum degeneracy. General expressions for a pair of equations of state, namely thermic (for the pressure) and caloric (for the inner energy) are found; the fluctuations of these quantities are also found: the compressibility and heat capacity, respectively. All expressions are found in closed form and studied in low- and high-temperature limits.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 6, pp. 167–199, 2009.
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Rudoy, Y.G., Rybakov, Y.P. & Keita, I. Thermodynamic pressure and its fluctuations in a classical ideal gas of relativistic particles. J Math Sci 172, 870–893 (2011). https://doi.org/10.1007/s10958-011-0230-0
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DOI: https://doi.org/10.1007/s10958-011-0230-0