Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics

Abstract

We review recent progress in developing effective field theories (EFTs) for non-equilibrium processes at finite temperature, including a new formulation of fluctuating 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 in equilibrium or near the vacuum. Secondly, while all static properties of an equilibrium system can in principle be extracted from the partition function, there appears no such quantity which can capture all non-equilibrium properties. Thirdly, non-equilibrium processes often involve dissipation, which is notoriously difficult to deal with using an action principle. The purpose of the review is to explain how to address these issues in a pedagogic manner, with fluctuating hydrodynamics as a main example.

36 pages, 4 figures

References in corpus (2)

• Negative local resistance caused by viscous electron backflow in graphene
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

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• The coset construction for non-equilibrium systems
• Spontaneous symmetry breaking and Nambu-Goldstone modes in open classical and quantum systems
• Elasticity bounds from Effective Field Theory
• Designing open quantum systems with known steady states: Davies generators and beyond
• Schwinger-Keldysh path integral for the quantum harmonic oscillator
• Non-equilibrium effective field theory and second sound
• Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media
• Spontaneous Symmetry Breaking, Spectral Statistics, and the Ramp
• Mapping GENERIC hydrodynamics into Carter's multifluid theory