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We derive relativistic hydrodynamics from quantum field theories by assumingthat the density operator is given by a local Gibbs distribution at initialtime. We decompose the energy-momentum tensor and particle current intonondissipative and dissipative parts, and analyze their time evolution indetail. Performing the path-integral formulation of the local Gibbsdistribution, we microscopically derive the generating functional for thenondissipative hydrodynamics.We also construct a basis to study dissipativecorrections. In particular, we derive the first-order dissipative hydrodynamicequations without a choice of frame such as the Landau-Lifshitz or Eckartframe.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method