title: The second laws of quantum thermodynamics.
abstract: 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.
authors: Department of Computer Science, University College London, London WC1E 6BT, United Kingdom;
authors: Fernando
authors: F
authors: Brandão
authors: Instytut Fizyki Teoretycznej i Astrofizyki, University of Gdansk, 80-952 Gdansk, Poland;
authors: Michał
authors: M
authors: Horodecki
authors: Centre for Quantum Technologies, National University of Singapore, 117543 Singapore;
authors: Nelly
authors: N
authors: Ng
authors: Centre for Quantum Technologies, National University of Singapore, 117543 Singapore; Department of Physics & Astronomy, University College London, London WC1E 6BT, United Kingdom; and j.oppenheim@ucl.ac.uk.
authors: Jonathan
authors: J
authors: Oppenheim
authors: Centre for Quantum Technologies, National University of Singapore, 117543 Singapore; School of Computing, National University of Singapore, 117417 Singapore.
authors: Stephanie
authors: S
authors: Wehner
keywords: free energy; quantum information theory; quantum thermodynamics; resource theory; statistical physics