Effective field theory for hydrodynamics: thermodynamics, and the
  derivative expansion
  We consider the low-energy effective field theory describing the infrared
dynamics of non-dissipative 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.
