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Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the…

Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum…

Statistical Mechanics · Physics 2009-11-10 A. E. Allahverdyan , R. Balian , Th. M. Nieuwenhuizen

Quantifying the ergotropy (a.k.a. available energy), namely the maximal amount of energy that can be extracted from a thermally isolated system, is a central problem in quantum thermodynamics. Notably, the same problem has been long studied…

Statistical Mechanics · Physics 2026-05-19 Michele Campisi

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however,…

Quantum Physics · Physics 2023-05-31 Dominik Šafránek , Dario Rosa , Felix Binder

Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work…

Quantum Physics · Physics 2022-05-18 Gianluca Francica

The paradigm of extracting work from isolated quantum system through a cyclic Hamiltonian process is a topic of immense research interest. The optimal work extracted under such process is termed as ergotropy [Europhys. Lett., 67 (4),…

Quantum Physics · Physics 2016-06-08 Amit Mukherjee , Arup Roy , Some Sankar Bhattacharya , Manik Banik

It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present…

Quantum Physics · Physics 2021-12-23 Akram Touil , Barış Çakmak , Sebastian Deffner

Ergotropy is defined as the maximum amount of work that can be extracted through a unitary cyclic evolution. It plays a crucial role in assessing the work capacity of a quantum system. Recently, the significance of quantum coherence in work…

Quantum Physics · Physics 2024-09-11 Zhibo Niu , Yang Wu , Yunhan Wang , Xing Rong , Jiangfeng Du

Entanglement entropy is one of the most prominent measures in quantum physics. We show that it has an interesting ergotropic interpretation in terms of unitarily extracted work. It determines how much energy one can extract from a source of…

Quantum Physics · Physics 2023-06-16 Dominik Šafránek

We introduce an ergotropy-based formulation of quantum thermodynamics, which provides a strong connection between average heat and von Neumann entropy. By adopting this formulation, we can reinterpret the infinitesimal average heat in terms…

Quantum Physics · Physics 2025-11-26 J. M. Z. Choquehuanca , P. A. C. Obando , M. S. Sarandy , F. M. de Paula

A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are…

Quantum Physics · Physics 2024-01-17 Amin Mohammadi , Afshin Shafiee

We study the maximal amount of energy that can be extracted from a finite quantum system by means of projective measurements. For this quantity we coin the expression "metrotropy" $\mathcal{M}$, in analogy with "ergotropy" $\mathcal{W}$,…

Quantum Physics · Physics 2019-09-10 Andrea Solfanelli , Lorenzo Buffoni , Alessandro Cuccoli , Michele Campisi

Ergotropy, the maximum work extractable from a quantum system, is a central resource in quantum physics. Computing ergotropy is well established when the system state is fully known, but its estimation under partial information remains an…

Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this…

Quantum Physics · Physics 2025-12-02 J. M. Z. Choquehuanca

Ergotropy, as a measure for extractable work from a quantum system, has garnered significant attention due to its relevance in quantum thermodynamics and information processing. In this work, the dynamics of ergotropy will be investigated…

Quantum Physics · Physics 2024-06-04 Maryam Hadipour , Soroush Haseli

Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite…

Quantum Physics · Physics 2025-01-27 Riccardo Castellano , Ranieri Nery , Kyrylo Simonov , Donato Farina

We propose a new form of the Second Law inequality that defines a tight bound for extractable work from the non-equilibrium quantum state. In classical thermodynamics, the optimal work is given by the difference of free energy, what…

Quantum Physics · Physics 2023-02-14 Marcin Łobejko

Extracting work from quantum system is one of the important areas in quantum thermodynamics. As a significant thermodynamic quantity, the ergotropy gap characterizes the difference between the global and local maximum extractable works. We…

Quantum Physics · Physics 2022-07-26 Ya-Juan Wu , Shao-Ming Fei , Zhi-Xi Wang , Ke Wu

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''.…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 A. E. Allahverdyan , R. Balian , Th. M. Nieuwenhuizen

The presence of correlations in the input state of a non-interacting many-body quantum system can lead to an increase in the amount of work we can extract from it under global unitary processes (ergotropy). The present work explore such…

Quantum Physics · Physics 2022-05-04 Raffaele Salvia , Vittorio Giovannetti
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