Hydrodynamics and the eightfold way to dissipation

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This is the first of two talks on recent advances in our understanding of hydrodynamics as a generic theory of near-thermal dynamics of density matrices. In this talk I will focus on the structure of the hydrodynamic gradient expansion subject to the Second Law of thermodynamics. I will present an eightfold classification scheme and an explicit solution at all orders in derivatives of hydrodynamic transport consistent with the Second Law. I will also mention some connections with gravity and argue that the classification hints towards the existence of a gauge theory whose symmetry current is the entropy current. (The topic of my second, independently accessible, talk on Nov 20 will be a detailed field theoretic proposal for how these and other interesting features emerge from microscopic Schwinger-Keldysh formalism.)