期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 112, 期 11, 页码 3275-3279出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1411728112
关键词
quantum thermodynamics; quantum information theory; statistical physics; resource theory; free energy
资金
- Royal Society
- Foundation for Polish Science TEAM project
- European Union European Regional Development Fund
- National Research Foundation
- Ministry of Education (MOE), Singapore
- MOE Grant Random numbers from quantum processes [MOE2012-T3-1-009]
- EPSRC [EP/J017280/1, EP/J017280/2, EP/K026313/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K026313/1, EP/J017280/2, EP/J017280/1] Funding Source: researchfish
The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.
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