Towards Hydrodynamics without an Entropy Current

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 correlation functions within the hydrodynamic derivative expansion without the need to explicitly solve the equations of hydrodynamics.