Linear response theory for the OTOC and entropy growth in dissipative systems.

We formulate the linear response theory to calculate the out-of-time ordered corralator (OTOC) and the entropy growth for dissipative systems, i.e. systems suddenly coupled to a thermal bath, which helps to understand the behavior of the information scrambling in the early stage. In addition, we also discuss the linear response of the OTOC to a perturbation for systems that are constantly coupled to a thermal bath and reaches the non-equilibrium static state. Particulary, we illustrated those calculations in the Dicke model.