Thermodynamic blocking in self-gravitating systems

TL;DR

The paper develops a thermodynamic framework to study self-gravitating systems, focusing on homogeneous configurations where kinetic theory (e.g., Balescu–Lenard) fails due to resonance and harmonicity. By formulating entropy and energy functionals that couple to the gravitational field via Poisson’s equation, the authors show that thermodynamic equilibria are entropy maxima and that homogeneous hydrostatic states exhibit thermodynamic blocking: entropy does not increase under adiabatic perturbations that preserve hydrostatic balance. This blocking applies in both 1D and 3D, with explicit analysis of first- and second-order variations and alternative derivations via barycenter conservation. The results highlight that, along the hydrostatic path, macroscopic matter and heat flows are suppressed, offering a thermodynamic mechanism for the slow relaxation observed in homogeneous self-gravitating systems and providing a complementary perspective to kinetic theories.

Abstract

Building upon a thermodynamic formalism, we show that self-gravitating systems in hydrostatic equilibrium with a uniform density are maximal entropy states when submitted to perturbations which are slow on dynamical timescale. We coin this phenomenon "thermodynamic blocking", given its similarity with the more general "kinetic blocking". This result underlines the importance of the thermodynamic formalism which proves useful when kinetic equations break down.