March 14, 2017
We revisit the problem of work extraction from a system in contact with a heat bath to a work storage system, and the reverse problem of state formation from a thermal system state in single-shot quantum thermodynamics. A physically intuitive and mathematically simple approach using only elementary majorization theory and matrix analysis is developed, and a graphical interpretation of the maximum extractable work, minimum work cost of formation, and corresponding single-shot free energies is presented. This approach provides a bridge between two previous methods based respectively on the concept of thermomajorization and a comparison of subspace dimensions. In addition, a conceptual inconsistency with regard to general work extraction involving transitions between multiple energy levels of the work storage system is clarified and resolved. It is shown that an additional contribution to the maximum extractable work in those general cases should be interpreted not as work extracted from the system, but as heat transferred from the heat bath. Indeed, the additional contribution is an artifact of a work storage system (essentially a suspended "weight" that can be raised or lowered) that does not truly distinguish work from heat. The result calls into question the common concept that a work storage system in quantum thermodynamics is simply the quantum version of a suspended weight in classical thermodynamics.
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April 20, 2015
This paper considers work extraction from a quantum system to a work storage system (or weight) following reference [1]. An alternative approach is here developed that relies on the comparison of subspace dimensions without a need to introduce thermo-majorisation used previously. Optimal single shot work for processes where a weight transfers from (a) a single energy level to another single energy level is then re-derived. In addition we discuss the final state of the system ...
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Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a `weight' that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and give a simple protocol to extract the optimal amount of work from the system, equal to its change in fre...
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We present a critical examination of the difficulties with the quantum versions of a lifted weight that are widely used as work storage systems in quantum thermodynamics. To overcome those difficulties, we turn to the strong connections between information and thermodynamics illuminated by Szilard's engine and Landauer's principle, and consider the concept of informational work storage. This concept is in sharp contrast with the usual one of mechanical work storage underlying...
February 12, 2013
We consider the task of extracting work from quantum systems in the resource theory perspective of thermodynamics, where free states are arbitrary thermal states, and allowed operations are energy conserving unitary transformations. Taking as our work storage system a 'weight' we prove the second law and then present simple protocols which extract average work equal to the free energy change of the system - the same amount as in classical thermodynamics. Crucially, for system...
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It has been recently claimed that no protocol for measuring quantum work can satisfy standard required physical principles, casting doubts on the compatibility between quantum mechanics, thermodynamics, and the classical limit. In this Letter, we present a solution for this incompatibility. We demonstrate that the standard formulation of these principles fails to address the classical limit properly. By proposing changes in this direction, we prove that all the essential prin...
February 14, 2004
A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''. 2) In work extraction from two-temperature setups, the presence of correlations can push the effective efficiency beyond the Carnot bound. 3) In the presence of level crossing, non-slow changes may be more optimal than slow ones.
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The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes -- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed ...
April 28, 2017
Free energy is energy that is available to do work. Maximizing the free energy gain and the gain in work that can be extracted from a system is important for a wide variety of physical and technological processes, from energy harvesting processes such as photosynthesis to energy storage systems such as fuels and batteries. This paper extends recent results from non-equilibrium thermodynamics and quantum resource theory to derive closed-form solutions for the maximum possible ...
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Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the possible transformations of open quantum systems. The foremost quantum thermodynamic law is a simple statement concerning the conservation of energy. Nevertheless, there exist ambiguity and disagreement regarding the precise partition of a quan...
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Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counterpart: the possibility of state transitions is not determined by free energy alone, but by an infinite family of free-energy-like quantities; strong fluctuations (possibly of quantum origin) allow to extract less work reliably than what is expected from computing the free energy difference. However, these known results rely crucially on the assumption that the thermal machine ...