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.

平衡态的稳定性是流体力学理论需要通过的关键测试之一。研究该性质的一种普遍技术包括以二次类能量函数的形式搜索线性化理论的李雅普诺夫函数。对于相对论流体，这种泛函的显式表达通常是通过猜测找到的，缺乏明确的物理解释。我们提出了一种基于最大熵原理的快速、严格和系统的技术，用于构建通用相对论流体理论的泛函。在泛函已知的情况下，该方法给出了预期的结果。为了使该方法适用，必须存在具有非负四散度的熵流。