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A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamicequilibrium in a uniformly accelerated frame of reference is studied usingGibbs's microcanonical and grand canonical formulations of statisticalmechanics. Using these methods explicit expressions for the particle, energyand entropy density distributions are obtained, which are found to be inagreement with the well known results of the relativistic formulation ofBoltzmann's kinetic theory. Explicit expressions for the total entropy, totalenergy and rest mass of the gas are obtained. The position of the center ofmass of the gas in equilibrium is found. The non-relativistic andultrarelativistic approximations are also considered. The phase space volume ofthe system is calculated explicitly in the ultrarelativistic approximation.

Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame