Excess-entropy scaling in gravitational systems

Phenomenological relations linking thermodynamics and kinetic theory in condensed matter have been empirically verified in numerous systems, yet their theoretical derivation from first principles remains an open question. One such relation is the so-called "excess-entropy scaling". Do N-body gravitational systems exhibit a similar relation? We provide an affirmative response to this question, albeit with some limitations. Our analysis relies on a well-established thermodynamical quasi-equilibrium model for the cosmological N-body problem, along with an appropriate diffusion model for gravitational interactions. By identifying a scaling region, we were able to estimate diffusion coefficients directly from observational two-particle correlation functions or counts-in-cells distributions in large-scale structures. Intriguingly, the phenomenon of excess-entropy scaling manifests primarily during the nonlinear, asymptotic clustering phase preceding a potential thermodynamic phase transition.