Resource theory of quantum states out of thermal equilibrium.
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.
Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, Minas Gerais 30123-970, Brazil and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
Fernando G S L
FG
Brandão
Institute for Theoretical Physics and Astrophysics, University of Gdańsk, PL-80952, Gdańsk, Poland and National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland.
Michał
M
Horodecki
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Jonathan
J
Oppenheim
Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstrasse 4a, 64289 Darmstadt, Germany and Institut für Theoretische Physik, ETH Zurich, CH-8093 Zürich, Switzerland.
Joseph M
JM
Renes
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Robert W
RW
Spekkens