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(Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional

Camille Aron, Giulio Biroli, Leticia F. Cugliandolo

SciPost Phys. 4, 008 (2018) · published 31 January 2018


We unveil the universal (model-independent) symmetry satisfied by Schwinger-Keldysh quantum field theories whenever they describe equilibrium dynamics. This is made possible by a generalization of the Schwinger-Keldysh path-integral formalism in which the physical time can be re-parametrized to arbitrary contours in the complex plane. Strong relations between correlation functions, such as the fluctuation-dissipation theorems, are derived as immediate consequences of this symmetry of equilibrium. In this view, quantum non-equilibrium dynamics -- e.g. when driving with a time-dependent potential -- are seen as symmetry-breaking processes. The symmetry-breaking terms of the action are identified as a measure of irreversibility, or entropy creation, defined at the level of a single quantum trajectory. Moreover, they are shown to obey quantum fluctuation theorems. These results extend stochastic thermodynamics to the quantum realm.

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Fluctuation-dissipation theorem Irreversibility Out-of-equilibrium systems Periodically-driven (Floquet) systems Schwinger-Keldysh method Stochastic thermodynamics Symmetry breaking

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