Applying the Gibbs stability criterion to relativistic hydrodynamics

Understand

The stability of the equilibrium state is one of the crucial tests a hydrodynamic theory needs to pass.

• A widespread technique to study this property consists of searching for a Lyapunov function of the linearised theory, in the form of a quadratic energy-like functional.
• For relativistic fluids, the explicit expression of such a functional is often found by guessing and lacks a clear physical interpretation.
• We present a quick, rigorous and systematic technique for constructing the functional of a generic relativistic fluid theory, based on the maximum entropy principle.