Speaker
Description
Hydrodynamics provides a universal description of the long-wavelength and low-frequency real-time dynamics of many-body systems near local thermal equilibrium. While its traditional formulation is based on conservation laws, thermodynamics, and a derivative expansion of constitutive relations, recent developments have revealed a unified field-theoretical framework underlying both deterministic and fluctuating hydrodynamics. In these lectures, I will first briefly review the phenomenological foundations of hydrodynamics and then discuss the quantum statistical mechanical formulation based on local Gibbs ensembles, with an emphasis on the imaginary-time (Matsubara) formalism for systems in local thermal equilibrium. I will then turn to fluctuating hydrodynamics and introduce the Schwinger–Keldysh formalism as a top-down effective field-theory framework that naturally incorporates dissipation, thermal fluctuations, and the symmetry principles governing nonequilibrium dynamics.