Stability and causality of Carter's multifluid theory

TL;DR

This paper investigates the stability and causality conditions of Carter's multifluid theory by analyzing linear perturbations, establishing a link between thermodynamic stability and causality, and identifying key stability criteria.

Contribution

It introduces a Lyapunov functional approach to assess stability and confirms that thermodynamic stability ensures causality in multifluid systems.

Findings

Entrainment matrix must be positive definite for stability

Thermodynamic stability implies linear causality

Lyapunov functional confirms stability criteria

Abstract

Stability and causality are studied for linear perturbations about equilibrium in Carter's multifluid theory. Our stability analysis is grounded on the requirement that the entropy of the multifluid, plus that of the environment, must be maximised at equilibrium. This allows us to compute a quadratic Lyapunov functional, whose positive definiteness implies stability. Furthermore, we verify explicitly that, also for multifluids, thermodynamic stability implies linear causality. As a notable stability condition, we find that the entrainment matrix must always be positive definite, confirming a widespread intuition.