Maximum entropy principle for quantum processes

The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a valuable choice as the system's state. An intriguing result is that in case the only prior knowledge is of a fixed mean energy, the maximum entropy state turns out to be the thermal state, a ubiquitous state in several arenas, especially in statistical mechanics. We extend the consequences of this principle from static quantum states to dynamic quantum processes. We establish that a quantum channel attains maximal entropy under a fixed mean energy constraint if and only if it is an absolutely thermalizing channel whose fixed output is the thermal state of the same mean energy. This provides an alternative approach for understanding the emergence of absolute thermalization processes within the observable part of the universe under physically natural energy constraints. Our results have potential implications for understanding the informational and thermodynamic utility of quantum channels under physical constraints. As an application, we examine the consequences for private randomness distillation from energy-constrained quantum processes.