Saddle-point entropy states of equilibrated self-gravitating systems

TL;DR

This paper analyzes the stability of equilibrium states in self-gravitating systems, revealing they are saddle points of entropy and proposing a two-phase relaxation process involving long- and short-range mechanisms.

Contribution

It introduces the concept that equilibrium states are saddle points of entropy and distinguishes between long- and short-range relaxation mechanisms in self-gravitating systems.

Findings

Equilibrium states are saddle points, not maxima or minima.

Two-phase violent relaxation: entropy production and decrease.

Long-wave Landau damping may be involved in the second phase.

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.