Coarse-grained distributions and superstatistics

TL;DR

This paper explores the connection between coarse-grained distributions in stellar systems and superstatistics, highlighting their similarities, differences, and implications for understanding statistical equilibria in astrophysical contexts.

Contribution

It introduces a novel link between violent relaxation distributions and superstatistics, clarifies distinctions among various entropy concepts, and compares equilibrium states in self-gravitating systems.

Findings

Established a connection between coarse-grained distributions and superstatistics.

Clarified the differences between various entropy measures.

Compared equilibrium states of different stellar system models.

Abstract

We show an interesting connexion between the coarse-grained distribution function arising in the theory of violent relaxation for collisionless stellar systems (Lynden-Bell 1967) and the notion of superstatistics introduced recently by Beck & Cohen (2003). We also discuss the analogies and differences between the statistical equilibrium state of a multi-components self-gravitating system and the metaequilibrium state of a collisionless stellar system. Finally, we stress the important distinction between mixing entropies, generalized entropies, H-functions, generalized mixing entropies and relative entropies.