Thermodynamics of a self-gravitating one-dimensional system with two unequal masses

Abstract

In this paper, we analyze the self-gravitating one-dimensional (1D) system with two particles of non-identical masses confined in a 1D box. This system is a simple toy model for the dynamics of halo stars. Exact expressions for the pressure, mean energy, and constant volume heat capacity are obtained using elementary methods. Several limiting cases are considered based on the interaction strength ε between the masses and their mass ratio α. For the weak interaction limit, i.e. ε → 0, the pressure and mean energy of the system approach the ideal gas limit. The simplicity of the calculations offers potential value for the model in introductory statistical physics courses.