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