A causal statistical family of dissipative divergence type fluids

TL;DR

This paper explores the causality properties of a class of relativistic dissipative fluids derived from statistical distributions, identifying subclasses that are manifestly causal both at and outside equilibrium.

Contribution

It introduces a simple causality condition for divergence type fluid theories derived from statistical distributions and identifies subclasses that are causally consistent.

Findings

Causality condition is simple for these fluid theories.

A subclass of theories is causally valid outside equilibrium.

Includes standard statistical distributions like Boltzmann, Bose, and Fermi.

Abstract

In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter, in the sense that the three tensor fields appearing in the theory can be expressed as the three first momenta of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperbolic partial differential equations is very simple and allow to identify a subclass of manifestly causal theories, which are so for all states outside equilibrium for which the theory preserves this statistical interpretation condition. This subclass includes the usual equilibrium distributions, namely Boltzmann, Bose or Fermi distributions, according to the statistics used, suitably generalized outside equilibrium. Therefore this gives a simple proof that they are causal in a neighborhood of equilibrium. We also find a bigger set of dissipative divergence type theories which are only pseudo-statistical, in the sense that the third rank tensor of the fluid theory has the symmetry and trace properties of a third momentum of an statistical distribution, but the energy-momentum tensor, while having the form of a second momentum distribution, it is so for a different distribution function. This set also contains a subclass (including the one already mentioned) of manifestly causal theories.