Thermodynamic pressure and its fluctuations in a classical ideal gas of relativistic particles

The full and consecutive analysis is carried on for 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. Gibbs statistical mechanics is used along with the Bogolyubov's concept of quasiaverages and the generalized version of Bogolyubov–Zubarev theorem in the classical regime well beyond the temperature of the quantum degeneracy. The general expressions are found for a pair of equations of state, namely thermic (for the pressure) and caloric (for the inner energy); 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.