  In this paper, we extend the fluctuation theorems used for quantum channels
to multitime processes. The fluctuation theorems for quantum channels are less
restrictive. We show that the given entropy production can be equal to the
result of a closed system environment. The assumption that the system evolves
under a completely positive and trace preserving map is quite general, but it
is more specific for cases in which the system is initially correlated with the
environment. System-environment correlations arise naturally in multitime
processes, with which we can give clear and physical interpretations regarding
the effects of correlations. Multitime processes can provide many-body
channels. The Choi state of such a many-body channel is called a process
tensor. One can derive channels by executing the process tensor on a set of
operations. We establish a general quantum fluctuation theorem framework for a
many-body channel and its derived channels. In this framework, the effects of
correlations are reflected in a Markovian property. For Markovian processes, we
can extend the two-point measurement to a three-point measurement and obtain
that the fluctuation theorems contain complete information about the
intermediate state. For non-Markovian processes, the complete measurement of
the intermediate state leads to conflicts. Therefore, we use a general
measurement, which only provides partial information, for the intermediate
state. The corresponding fluctuation theorems show that memory effects can
reduce these fluctuations. This is consistent with the fact that system states
can be recovered under non-Markovian processes.
