Microcanonical density of states of a hard-particle fluid under gravity

A simple approximate expression is proposed for the energy dependence of the microcanonical density of states of a classical hard-particle fluid column of infinite height in a uniform gravitational field. This expression is based on the exact result in one dimension and depends on an effective parameter that can be related to the mean kinetic energy in the fluid. The behavior of this parameter is investigated by means of molecular dynamics simulations, showing an asymptotically linear regime at high energies. From the density of states an approximate expression is obtained for the microcanonical single-particle momentum modulus distribution function. By comparing the results of this approximation with simulation data for a hard-disk fluid it is found that the energy dependence proposed for the density of states is a very good approximation for a wide range of values of the characteristic parameters of the system.