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.