Applying the Gibbs stability criterion to relativistic hydrodynamics

The stability of the equilibrium state is one crucial tests a hydrodynamic theory needs to pass. A widespread technique study this property consists searching for Lyapunov function linearised theory, in form quadratic energy-like functional. For relativistic fluids, explicit expression such functional often found by guessing and lacks clear physical interpretation. We present quick, rigorous systematic constructing generic fluid based on maximum entropy principle. method gives expected result those cases which was already known. be applicable, there must an current with non-negative four-divergence. This important step towards definitive resolution major open problems connected dissipation.