Special relativistic effects in the equilibrium statistical mechanics of the one dimensional gravitational gas and the Takahashi gas

Abstract

We calculate the partition function of the relativistic one-dimensional gas for various potentials. We consider two possible interactions between the particles of the gas: the one-dimensional relativistic gravitational gas, and the relativistic Takahashi nearest-neighbor gas. We also show how the internal energy, the equation of state, and the heat capacity at constant volume may be calculated.