Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1603.02417 · Nature Communications

Work extraction from quantum systems with bounded fluctuations in work

Jonathan G. Richens, Lluís Masanes

Published Nov 25, 2016• 33 citations
arXivHTMLPDF

Abstract

In the standard framework of thermodynamics, work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. Here we show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount c. By varying c we interpolate between the standard and minimum free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations.

DOI
10.1038/ncomms13511

Related papers

Surpassing the Carnot efficiency by extracting imperfect work

Nelly Huei Ying Ng, Mischa P. Woods, Stephanie Wehner

A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of 'work' is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be done without using any additional resources such as coherence or correlations, and furthermore can be achieved even when one of the heat baths is finite in size.

arXiv:1606.05532•New Journal of Physics•Sep 15, 2017•32 citations

Theoretical Study of Controlling Nonequilibrium Systems using Fluctuation Theorems and Trade-off Relations

謙 布能

Recent developments of the analysis of the second law of thermodynamics by using the information theoretic quantities has led to the discovery of the so-called nonequilibrium free energy and has allowed us to formulate thermodynamic relations for arbitrary nonequilibrium initial and final states.By using the nonequilibrium free energies, we can quantify thermodynamic costs of information encoding and erasure processes as well as to quantify the extractable work from information heat engines in a unified way.In those general situations, reducing dissipation allows us to increase the extractable work from the system (or to reduce the work cost), and reducing work fluctuation allows us to narrow the work probability distribution and to extract a fluctuation-free work from the system.Suppressing both work fluctuation and dissipation as much as possible is vital to control mesoscopic and nano systems that work at the level of thermal fluctuations.Previous studies have searched for a vanishing work fluctuation protocol by using techniques of quantum information theory, known as the single-shot statistical mechanics (and sometimes called the deterministic work extraction protocol) and the vanishing dissipation protocol, known as the thermodynamically reversible protocol by using the second law of thermodynamics.In this thesis, we address issues concerning a method to control nonequilibrium systems by using fluctuation theorems and trade-off relation between work fluctuation and fluctuation in dissipation.We derive quantum fluctuation theorems under measurement and feedback control, which allow us to study how to suppress dissipation during a general quantum measurement and a feedback control.We then consider a method to suppress work fluctuation and fluctuation in dissipation simultaneously as much as possible by showing the trade-off relation between work and dissipation in terms of their standard deviations and derive an explicit protocol that achieves the lower bound of the trade-off relation.We show that the explicit protocol reproduces the deterministic work extraction protocol in the limit of vanishing work fluctuation and the thermodynamically reversible protocol in the limit of vanishing fluctuation in dissipation.

•Apr 28, 2016•0 citations

Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

Michele Campisi, Jukka Pekola, Rosario Fazio

We study stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency greater than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) are illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid-state implementations with Cooper-pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.

arXiv:1412.0898•New Journal of Physics•Mar 20, 2015•216 citations

Attaining Carnot efficiency with quantum and nanoscale heat engines

Mohit Lal Bera, Maciej Lewenstein, Manabendra Nath Bera

Abstract A heat engine operating in the one-shot finite-size regime, where systems composed of a small number of quantum particles interact with hot and cold baths and are restricted to one-shot measurements, delivers fluctuating work. Further, engines with lesser fluctuation produce a lesser amount of deterministic work. Hence, the heat-to-work conversion efficiency stays well below the Carnot efficiency. Here we overcome this limitation and attain Carnot efficiency in the one-shot finite-size regime, where the engines allow the working systems to simultaneously interact with two baths via the semi-local thermal operations and reversibly operate in a one-step cycle. These engines are superior to the ones considered earlier in work extraction efficiency, and, even, are capable of converting heat into work by exclusively utilizing inter-system correlations. We formulate a resource theory for quantum heat engines to prove the results.

arXiv:1911.07003•npj Quantum Information•Feb 12, 2021•24 citations

Optimal processes for probabilistic work extraction beyond the second law

Vasco Cavina, Andrea Mari, Vittorio Giovannetti

According to the second law of thermodynamics, for every transformation performed on a system which is in contact with an environment of fixed temperature, the average extracted work is bounded by the decrease of the free energy of the system. However, in a single realization of a generic process, the extracted work is subject to statistical fluctuations which may allow for probabilistic violations of the previous bound. We are interested in enhancing this effect, i.e. we look for thermodynamic processes that maximize the probability of extracting work above a given arbitrary threshold. For any process obeying the Jarzynski identity, we determine an upper bound for the work extraction probability that depends also on the minimum amount of work that we are willing to extract in case of failure, or on the average work we wish to extract from the system. Then we show that this bound can be saturated within the thermodynamic formalism of quantum discrete processes composed by sequences of unitary quenches and complete thermalizations. We explicitly determine the optimal protocol which is given by two quasi-static isothermal transformations separated by a finite unitary quench.

arXiv:1604.08094•Scientific Reports•Jul 5, 2016•21 citations

The extraction of work from quantum coherence

Kamil Korzekwa, Matteo Lostaglio, Jonathan Oppenheim +1 more

The interplay between quantum-mechanical properties, such as coherence, and classical notions, such as energy, is a subtle topic at the forefront of quantum thermodynamics. The traditional Carnot argument limits the conversion of heat to work; here we critically assess the problem of converting coherence to work. Through a careful account of all resources involved in the thermodynamic transformations within a fully quantum-mechanical treatment, we show that there exist thermal machines extracting work from coherence arbitrarily well. Such machines only need to act on individual copies of a state and can be reused. On the other hand, we show that for any thermal machine with finite resources not all the coherence of a state can be extracted as work. However, even bounded thermal machines can be reused infinitely many times in the process of work extraction from coherence.

arXiv:1506.07875•New Journal of Physics•Feb 18, 2016•313 citations
In the standard framework of thermodynamics, work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. Here we show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount c. By varying c we interpolate between the standard and minimum free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations.
A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of 'work' is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be done without using any additional resources such as coherence or correlations, and furthermore can be achieved even when one of the heat baths is finite in size.
Recent developments of the analysis of the second law of thermodynamics by using the information theoretic quantities has led to the discovery of the so-called nonequilibrium free energy and has allowed us to formulate thermodynamic relations for arbitrary nonequilibrium initial and final states.By using the nonequilibrium free energies, we can quantify thermodynamic costs of information encoding and erasure processes as well as to quantify the extractable work from information heat engines in a unified way.In those general situations, reducing dissipation allows us to increase the extractable work from the system (or to reduce the work cost), and reducing work fluctuation allows us to narrow the work probability distribution and to extract a fluctuation-free work from the system.Suppressing both work fluctuation and dissipation as much as possible is vital to control mesoscopic and nano systems that work at the level of thermal fluctuations.Previous studies have searched for a vanishing work fluctuation protocol by using techniques of quantum information theory, known as the single-shot statistical mechanics (and sometimes called the deterministic work extraction protocol) and the vanishing dissipation protocol, known as the thermodynamically reversible protocol by using the second law of thermodynamics.In this thesis, we address issues concerning a method to control nonequilibrium systems by using fluctuation theorems and trade-off relation between work fluctuation and fluctuation in dissipation.We derive quantum fluctuation theorems under measurement and feedback control, which allow us to study how to suppress dissipation during a general quantum measurement and a feedback control.We then consider a method to suppress work fluctuation and fluctuation in dissipation simultaneously as much as possible by showing the trade-off relation between work and dissipation in terms of their standard deviations and derive an explicit protocol that achieves the lower bound of the trade-off relation.We show that the explicit protocol reproduces the deterministic work extraction protocol in the limit of vanishing work fluctuation and the thermodynamically reversible protocol in the limit of vanishing fluctuation in dissipation.
We study stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency greater than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) are illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid-state implementations with Cooper-pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.
Abstract A heat engine operating in the one-shot finite-size regime, where systems composed of a small number of quantum particles interact with hot and cold baths and are restricted to one-shot measurements, delivers fluctuating work. Further, engines with lesser fluctuation produce a lesser amount of deterministic work. Hence, the heat-to-work conversion efficiency stays well below the Carnot efficiency. Here we overcome this limitation and attain Carnot efficiency in the one-shot finite-size regime, where the engines allow the working systems to simultaneously interact with two baths via the semi-local thermal operations and reversibly operate in a one-step cycle. These engines are superior to the ones considered earlier in work extraction efficiency, and, even, are capable of converting heat into work by exclusively utilizing inter-system correlations. We formulate a resource theory for quantum heat engines to prove the results.
According to the second law of thermodynamics, for every transformation performed on a system which is in contact with an environment of fixed temperature, the average extracted work is bounded by the decrease of the free energy of the system. However, in a single realization of a generic process, the extracted work is subject to statistical fluctuations which may allow for probabilistic violations of the previous bound. We are interested in enhancing this effect, i.e. we look for thermodynamic processes that maximize the probability of extracting work above a given arbitrary threshold. For any process obeying the Jarzynski identity, we determine an upper bound for the work extraction probability that depends also on the minimum amount of work that we are willing to extract in case of failure, or on the average work we wish to extract from the system. Then we show that this bound can be saturated within the thermodynamic formalism of quantum discrete processes composed by sequences of unitary quenches and complete thermalizations. We explicitly determine the optimal protocol which is given by two quasi-static isothermal transformations separated by a finite unitary quench.
The interplay between quantum-mechanical properties, such as coherence, and classical notions, such as energy, is a subtle topic at the forefront of quantum thermodynamics. The traditional Carnot argument limits the conversion of heat to work; here we critically assess the problem of converting coherence to work. Through a careful account of all resources involved in the thermodynamic transformations within a fully quantum-mechanical treatment, we show that there exist thermal machines extracting work from coherence arbitrarily well. Such machines only need to act on individual copies of a state and can be reused. On the other hand, we show that for any thermal machine with finite resources not all the coherence of a state can be extracted as work. However, even bounded thermal machines can be reused infinitely many times in the process of work extraction from coherence.