Saddle-point entropy states of equilibrated self-gravitating systems

Abstract

In this Letter, we investigate the stability of the statistical equilibrium of spherically symmetric collisionless self-gravitating systems. By calculating the second variation of the entropy, we find that perturbations of the relevant physical quantities should be classified as long- and short-range perturbations, which correspond to the long- and short-range relaxation mechanisms, respectively. We show that the statistical equilibrium states of self-gravitating systems are neither maximum nor minimum, but complex saddle-point entropy states, and hence differ greatly from the case of ideal gas. Violent relaxation should be divided into two phases. The first phase is the entropy-production phase, while the second phase is the entropy-decreasing phase. We speculate that the second-phase violent relaxation may just be the long-wave Landau damping, which would work together with short-range relaxations to keep the system equilibrated around the saddle-point entropy states.

5 pages, 1 figure, MNRAS Letter, in the press

References in corpus (4)

• The Diversity and Similarity of Simulated Cold Dark Matter Halos
• Secondary Infall and the Pseudo-Phase-Space Density Profiles of Cold Dark Matter Halos
• Entropy principle and complementary second law of thermodynamics for self-gravitating systems
• A statistical-mechanical explanation of dark matter halo properties

Cited by in corpus (4)

• Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics
• Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample
• Fluid-like entropy and equilibrium statistical mechanics of self-gravitating systems
• Second-order solutions of the equilibrium statistical mechanics for self-gravitating systems