  We present a generating functional which describes the equilibrium
thermodynamic response of a relativistic system to external sources. A
variational principle gives rise to constraints on the response parameters of
relativistic hydrodynamics without making use of an entropy current. Our method
reproduces and extends results available in the literature. It also provides a
technique for efficiently computing n-point zero-frequency hydrodynamic
correlation functions without the need to solve the equations of hydrodynamics.
