thermodynamic properties of strongly gravitating systems

This paper investigates the thermodynamic properties of strongly interacting gravitational systems. by deriving the partition function for such systems, the authors obtain expressions for various thermodynamic quantities, including internal energy, specific heat, helmholtz free energy, entropy, chemical potential, and pressure. the paper introduces an interaction parameter that quantifies the degree of non-ideality in the system, and explores its effects on the thermodynamic properties. the authors also calculate the moments generating function, which provides information about the distribution of particle positions. additionally, the distribution function for the system is derived. the paper highlights the existence of an upper bound temperature beyond which the partition function becomes negative, indicating a limit on the validity of the model.