Thermodynamic stability implies causality

TL;DR

This paper demonstrates that in relativistic hydrodynamics, thermodynamic stability ensures causality, establishing that stable theories cannot allow signals to propagate outside the light-cone, thus linking entropy maximization with causal behavior.

Contribution

The authors prove that thermodynamic stability in relativistic hydrodynamics implies causality, extending the connection between entropy and information to finite temperature and chemical potential.

Findings

Stable relativistic hydrodynamic theories are causal.

Acausal theories are thermodynamically unstable.

The work generalizes the Hawking-Ellis vacuum conservation theorem.

Abstract

The stability conditions of a relativistic hydrodynamic theory can be derived directly from the requirement that the entropy should be maximised in equilibrium. Here we use a simple geometrical argument to prove that, if the hydrodynamic theory is stable according to this entropic criterion, then localised perturbations to the equilibrium state cannot propagate outside their future light-cone. In other words, within relativistic hydrodynamics, acausal theories must be thermodynamically unstable, at least close to equilibrium. We show that the physical origin of this deep connection between stability and causality lies in the relationship between entropy and information. Our result may be interpreted as an ``equilibrium conservation theorem'', which generalizes the Hawking-Ellis vacuum conservation theorem to finite temperature and chemical potential.