New Entry in the Thermodynamic Rulebook for Quantum Systems

Abstract

Thermodynamic laws that are unique to quantum systems in a superposition of states have been derived using an information-theory approach. Physicists are developing new experimental tools to build engines, refrigerators, and other thermodynamic machines with quantum components. Such machines are not only small, but they might also possess unex-pected capabilities compared to their classical counter-parts. Finding the fundamental limits on how these ma-chines operate—a set of thermodynamic laws that apply on the quantum scale—is therefore an important theoret-ical goal. In independent papers, Piotr Ćwikliński from the University of Gdansk, Poland [1], and colleagues, and Matteo Lostaglio at Imperial College, UK, and colleagues [2] have derived a set of such laws, akin to the second law, for quantum systems that exist in a coherent superposi-tion of states. These laws spell out the restrictions for how such a system can evolve under any physically plau-sible operation, thus providing ultimate limitations that even quantum machines cannot overcome. Theoretical thermodynamics has always been practi-cally motivated. Its aim is to develop principles that tell us what types of machines we can build, and the limits on their efficiency and output. Our ability to manipu-late a system depends on the information we have about its state. Recent efforts to understand the thermody-namics of quantum systems have therefore been inspired by quantum information theory [3], a field perhaps best known in connection with quantum cryptography and computing. In this context, thermodynamic descriptions involve very little information. Thermodynamic theory of clas-sical systems assumes we can't know the microstates of each constituent in a large collection of particles, but only some average quantities, like a system's total internal en-ergy. When such a system is in thermal equilibrium with its environment, we can, however, describe it in terms of a single parameter: the temperature. Since entropy quantifies a lack of information, this reductive descrip-tion corresponds to the one with the greatest possible entropy still compatible with a specified internal energy. A system described by such thermal states is therefore said to serve as a " ubiquitous " resource for machines, because no assumption is made about its internal work-ings. And any operation that requires more knowledge of the system—say, knowing the positions of each atom in a gas—is impossible. Thermalization is also an important notion in the quantum regime [4], and machines operating at such scales can also take advantage of thermal resources. The thermal-resource-theory approach to quantum thermo-dynamics aims to identify which operations are feasi-ble and which ones are impossible. In this framework, thermal operations define all actions a quantum system can perform, with the restriction that the total energy of the machine and its thermal environment must be con-served—the dictum of the first law of thermodynamics. The set of all such operations thus functions as a sort of " rule book " for physical processes. The resource-theory approach has been used for clas-sical systems to derive the second law of thermodynam-ics from microscopic principles. Unlike classical systems, however, quantum systems have the added complexity that they have discretized energy levels and can exist in coherent superpositions of different states. So far, the resource-theory approach has been used to find a whole family of second-law-like restrictions for quantum