Resource Theory of Quantum States Out of Thermal Equilibrium

TLDR

Thermodynamics in quantum information theory identifies certain states as resources when transformations are restricted, with entanglement being the most studied example. The authors apply resource‑theoretic methods to thermodynamics, showing that free energy naturally arises from energy‑preserving transformations. They find that free energy measures the useful work extractable from many copies of a quantum system under reversible energy‑preserving operations with a thermal bath, and also quantifies the asymptotic reversible interconversion rate of resource states when a sublinear amount of coherent superposition over energy levels is available.

Abstract

The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically-many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.