  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. The method gives the
expected result in those cases in which the functional was already known. For
the method to be applicable, there must be an entropy current with non-negative
four-divergence. This result is an important step towards a definitive
resolution of the major open problems connected with relativistic dissipation.
