Adjoint master equation for multitime correlators

The quantum regression theorem is a powerful tool for calculating the multitime correlators of operators of open quantum systems whose dynamics can be described in Markovian approximation. However, the scope of the quantum regression theorem is limited by a particular time order of the operators in multitime correlators and does not include out-of-time-ordered correlators. In this work, we obtain an adjoint master equation for multitime correlators that applies to out-of-time-ordered correlators. We show that this equation can be derived for various approaches to the description of the dynamics of open quantum systems, such as the global or local approach. We show that the adjoint master equation for multitime correlators is self-consistent. Namely, the final equation does not depend on how the operators are grouped inside the correlator and it coincides with the quantum regression theorem for the particular time ordering of the operators.