Thermodynamic Capacity of Quantum Processes

Abstract: Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state---as for instance in the case of an ideal gas---the possible transformations become reversible and are fully characterized by the free energy. In this Letter, we present a thermodynamic resource theory for quantum processes that also becomes reversible in the macroscopic limit, a property that is especially rare for a resource theory of quantum channels. We identify a unique single-letter and additive quantity, the thermodynamic capacity, that characterizes the "thermodynamic value" of a quantum channel, in the sense that the work required to simulate many repetitions of a quantum process employing many repetitions of another quantum process becomes equal to the difference of the respective thermodynamic capacities. On a technical level, we provide asymptotically optimal constructions of universal implementations of quantum processes. A challenging aspect of this construction is the apparent necessity to coherently combine thermal engines that would run in different thermodynamic regimes depending on the input state. Our results have applications in quantum Shannon theory by providing a generalized notion of quantum typical subspaces and by giving an operational interpretation to the entropy difference of a channel.