The second laws of quantum thermodynamics
17 Mar 2015-Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences)-Vol. 112, Iss: 11, pp 3275-3279
TL;DR: Here, it is found 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.
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.
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28,685 citations
TL;DR: This paper introduced a new development in theoretical quantum physics, the ''resource-theoretic'' point of view, which aims to be closely linked to experiment, and to state exactly what result you can hope to achieve for what expenditure of effort in the laboratory.
Abstract: This review introduces a new development in theoretical quantum physics, the ``resource-theoretic'' point of view. The approach aims to be closely linked to experiment, and to state exactly what result you can hope to achieve for what expenditure of effort in the laboratory. This development is an extension of the principles of thermodynamics to quantum problems; but there are resources that would never have been considered previously in thermodynamics, such as shared knowledge of a frame of reference. Many additional examples and new quantifications of resources are provided.
841 citations
Cites background or methods from "The second laws of quantum thermody..."
...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)....
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...More precisely, it would be possible to freely generate any density matrix ρ to arbitrary precision by consuming many copies of σ (Brandão et al., 2015a; Yunger Halpern and Renes, 2016)....
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...Whereas macroscopic state transfor- mations via heat exchange are essentially governed by a decrease in free energy, in the quantum regime, more constraints dictate whether or not a given transformation is possible (Brandão et al., 2015a; Gour et al., 2018b; Horodecki and Oppenheim, 2013a)....
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TL;DR: Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit.
Abstract: Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects Fuelled by experimental advances and the potential of future nanoscale applications this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of "work", to the efficiency and power of quantum engines This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike
732 citations
TL;DR: It is shown that free energy relations cannot properly describe quantum coherence in thermodynamic processes, and it is found that coherence transformations are always irreversible.
Abstract: Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilard engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement. The statistical nature of standard thermodynamics provides an incomplete picture for individual processes at the nanoscale, and new relations have been developed to extend it. Here, the authors show that by quantifying time-asymmetry it is also possible to characterize how quantum coherence is modified in such processes.
664 citations
Cites background from "The second laws of quantum thermody..."
...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:...
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40,330 citations
"The second laws of quantum thermody..." refers background in this paper
...This criterion has been conjectured [10] and claimed to be [7] a second law....
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...The quantity on the right hand side of Equation (7) can also be thought of as a distance measure between states, as was done with the thermo-majorisation criteria in [7] and we will henceforth refer to it as the work distance from ρ to ρ′....
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Journal Article•
28,685 citations
"The second laws of quantum thermody..." refers background in this paper
...Due to the non-commutative nature of the state of the system and the thermal state, our new free energies have a more complicated form and are based on quantum Renyi divergences [14–16] (see also [17])....
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...In [15, 16] (see also [17]) another version of the quantum divergence was introduced for α ∈ (0,∞]: Sα(ρ||σ) = 1 α− 1 log ( tr(σ 1−α 2α ρσ 1−α 2α ) ) (A13)...
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Book•
06 Apr 2011
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Abstract: Introduction.- Doubly Stochastic Matrices.- Schur-Convex Functions.- Equivalent Conditions for Majorization.- Preservation and Generation of Majorization.- Rearrangements and Majorization.- Combinatorial Analysis.- Geometric Inequalities.- Matrix Theory.- Numerical Analysis.- Stochastic Majorizations.- Probabilistic, Statistical, and Other Applications.- Additional Statistical Applications.- Orderings Extending Majorization.- Multivariate Majorization.- Convex Functions and Some Classical Inequalities.- Stochastic Ordering.- Total Positivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.
6,641 citations
TL;DR: Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.
Abstract: It is argued that computing machines inevitably involve devices which perform logical functions that do not have a single-valued inverse. This logical irreversibility is associated with physical irreversibility and requires a minimal heat generation, per machine cycle, typically of the order of kT for each irreversible function. This dissipation serves the purpose of standardizing signals and making them independent of their exact logical history. Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.
3,629 citations
"The second laws of quantum thermody..." refers background in this paper
...The reason that such fine control does not lead to a violation of the second law is related to the fact that a Maxwell’s demon with microscopic control over a system cannot violate the second law––a demon which knows the positions and momenta of the particles of a system, must record this information in a memory, which then needs to be reset at the end of a cyclic process (34, 35)....
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TL;DR: Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.
Abstract: If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly entangled pure states, one member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally entangled pairs of particles, for example, Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves entropy of entanglement---the von Neumann entropy of the partial density matrix seen by either observer---with the yield of singlets approaching, for large n, the base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement. \textcopyright{} 1996 The American Physical Society.
2,633 citations