THE THERMODYNAMIC DESCRIPTION OF THE COSMOLOGICAL MANY-BODY PROBLEM

We investigate three fundamental aspects of the thermodynamic descript ion of the cosmological many-body problem, which has been used extensi vely as a model of galaxy clustering. First we show explicitly how the thermodynamic description involves only the local fluctuating part of the gravitational field, even though gravity is a long-range force. S econd we discuss the conditions for a quasi-equilibrium description to apply. Third, we derive the functional form of b((n) over bar, T), th e ratio of gravitational correlation energy to twice the kinetic energ y of peculiar velocities, which completes the equation of state. This functional form previously had to be postulated as an Ansatz. We also discuss how it is related to other physical properties of the system.