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

## TL;DR

This paper reveals a universal symmetry in equilibrium quantum field theories using a generalized Schwinger-Keldysh formalism, linking correlation functions, irreversibility, and quantum fluctuation theorems, thus extending stochastic thermodynamics to quantum systems.

## Contribution

It introduces a generalized formalism that uncovers a universal symmetry in equilibrium quantum dynamics and relates symmetry-breaking to irreversibility and quantum fluctuation theorems.

## Key findings

- Derivation of fluctuation-dissipation relations from the symmetry
- Identification of symmetry-breaking terms as entropy production
- Extension of stochastic thermodynamics principles to quantum systems

## Abstract

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.