Cavity Volume and Free Energy in Many-Body Systems

Within this work we derive and analyse an expression for the free energy of a single-species system in thermodynamic limit terms generalised cavity volume, that is exact general, principle applicable to systems across their entire range density, as well particles within general coordinate space. This provides universal equation state, can thus relate volume classical results, such Mayer's cluster expansions. Through are able provide some insight into connections between consequences. We use examples which permit explicit computations further probe these reclaiming results Tonks gas providing novel derivation Onsager's single species, isotropic system. Given complexity problem also local lattice ansatz, one dimension, with may approximate hard sphere accurate state cases disks spheres both dilute regimes beyond freezing transition.