  We introduce a subsystem generalization of the spectral form factor via
pseudo entropy, the von-Neumann entropy for the reduced transition matrix. We
consider a transition matrix between the thermofield double state and its
time-evolved state in two-dimensional conformal field theories, and study the
time-dependence of the pseudo entropy for a single interval. We show that the
real part of the pseudo entropy behaves similarly to the spectral form factor;
it starts from the thermal entropy, initially drops to the minimum, then it
starts increasing, and finally approaches the vacuum entanglement entropy. We
also study the theory-dependence of its behavior by considering theories on a
compact space.
