The second laws of quantum thermodynamics

By Fernando G. S. L. Brandão, Michal Horodecki, Nelly Huei Ying Ng, Jonathan Oppenheim, Stephanie Wehner. Proceedings of the National Academy of Sciences of the United States of America, 2013

724 citations recorded by the source corpus.

Significance In ordinary thermodynamics, transitions are governed by a single quantity–the free energy. Its monotonicity is a formulation of the second law. Here, we find that the second law for microscopic or highly correlated systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on state transformations, but many. We find a family of quantum free energies which generalize the standard free energy, and can never increase. The ordinary second law corresponds to the nonincreasing of one of these free energies, with the remainder imposing additional constraints on thermodynamic transitions. In the thermodynamic limit, these additional second laws become equivalent to the standard one. We also prove a strengthened version of the zeroth law of thermodynamics, allowing a definition of temperature. 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27701d2cc7a7b598a980437661599d8247b4c95e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

The role of quantum coherence in non-equilibrium entropy production (2017, methodology): “Other approaches have also been used elsewhere [42, 43].”
Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, background): “As a consequence of equation (21) and the definition of Fa, if all Fa decrease the purity measures in the embedding space will decrease as well:”
A mathematical theory of resources (2014, positive): “g many results in quantum thermodynamics, including the limits to work extraction [13,28,44], Landauer’s solution to the Maxwell demon problem [25], and the status of the second law of thermodynamics [25,12]. Note that there are strong parallels between the resource theories that arise in this way, ”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “At the same time, further interconnections to thermal operations [92, 294, 395] and resource theory [394] will emerge by quantifying benefits and limits of heat-bath coupling [22] in terms of reachable sets.”
Quantum resource theories (2018, methodology): “In particular, by adopting a QRT perspective, the four Laws of Thermodynamics can be stated more precisely, and the relationships between them can be made more apparent (Brandão et al., 2015a; Masanes and Oppenheim, 2017).”
Quantum coherence, time-translation symmetry and thermodynamics (2014, background): “measures provides necessary and sufficient conditions when the states are incoherent in energy (free energies Fα, parametrized by a real number α, must all decrease [5]).”
Irreversible entropy production: From classical to quantum (2020, methodology): “This was first addressed in (Åberg, 2013) and then in more detail in (Brandão et al., 2015; Horodecki and Oppenheim, 2013).”