Effective field theory for hydrodynamics: Thermodynamics, and the derivative expansion

We consider the low-energy effective field theory describing the infrared dynamics of nondissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field-theory variables and thermodynamical ones. We discuss the systematics of the derivative expansion, for which field theory offers a conceptually clear and technically neat scheme. As an example, we compute the correction to the sound-wave dispersion relation coming from a sample second-order term. This formalism forms the basis for a study of anomalies in hydrodynamics via effective field theory, which is initiated in a companion paper.