  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.

Statistical Mechanics;High Energy Physics - Theory;Quantum Physics