Maximum entropy principle for quantum processes

Abstract: The maximum entropy principle states that the maximum entropy among all quantum states with a fixed mean energy is achieved only by the thermal state of given mean energy. In this notes, we prove the maximum entropy principle for quantum processes -- the entropy of a quantum channel with fixed mean energy is maximum if and only if the channel is absolutely thermalizing channel with the fixed output thermal state of that mean energy. This allows for an alternate approach to describe emergence of the absolute thermalization processes under energy constraints in the observable universe.