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We review recent progress in developing effective field theories (EFTs) fornon-equilibrium processes at finite temperature, including a new formulation offluctuating hydrodynamics, and a new proof of the second law of thermodynamics.There are a number of new elements in formulating EFTs for such systems.Firstly, the nature of IR variables is very different from those of a system inequilibrium or near the vacuum. Secondly, while all static properties of anequilibrium system can in principle be extracted from the partition function,there appears no such quantity which can capture all non-equilibriumproperties. Thirdly, non-equilibrium processes often involve dissipation, whichis notoriously difficult to deal with using an action principle. The purpose ofthe review is to explain how to address these issues in a pedagogic manner,with fluctuating hydrodynamics as a main example.

Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics