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:1710.09444 · Physical review. E

Fluctuation relation for heat exchange in Markovian open quantum systems

Mehdi Ramezani, Mehdi Golshani, A. T. Rezakhani

Published Apr 2, 2018• 8 citations
arXivHTMLPDF

Abstract

A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. Interestingly, this relation is akin to the standard form of the fluctuation relation (for forward-backward dynamics). We also argue that the probability of the violation of the second law of thermodynamics in the form of the Clausius statement (i.e., net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences of the baths.

DOI
10.1103/physreve.97.042101

Related papers

Exchange Fluctuation Theorems for Non-Markovian Baths in Quantum Collisional Model

Sayan Mondal, Sukrut Mondkar, Ujjwal Sen

The quantum exchange fluctuation theorem relates the probabilities of observing heat transfer along and against the temperature gradient between thermal baths at different temperatures. We investigate how this relation generalizes when the baths exhibit non-Markovian dynamics. Using a microscopic collisional model, bath memory is generated through interactions between successive bath auxiliaries before each heat-exchange collision. We derive exchange fluctuation theorems for both direct bath-bath interactions and probe-mediated heat exchange in the steady-state regime. As an illustrative example, we consider heat baths with qubit auxiliaries and show that non-Markovian memory enhances the probability of heat-transfer events against the temperature gradient, modifying the predictions made by the conventional Jarzynski-Wójcik exchange fluctuation theorem. Our results establish a microscopic connection between environmental memory and non-equilibrium heat-exchange statistics.

quant-pharXiv:2608.11488•Aug 13, 2026•0 citations

Stochastic thermodynamics of a finite quantum system coupled to two heat baths

Heinz–Jürgen Schmidt, Jochen Gemmer B

We consider a situation where an $N$-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general Jarzinski-type equation and conclude that heat and entropy is flowing from the hot bath to the cold one. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities. Our approach is illustrated by an analytical example. For the linear regime, i.~e., for small temperature differences between the two heat baths we derive an expression for the heat conduction coefficient.

arXiv:2108.02805•Aug 5, 2021•0 citations

Generalized Quantum Fluctuation Theorem for Energy Exchange

Wei Wu, Jun‐Hong An

The nonequilibrium fluctuation relation is a cornerstone of quantum thermodynamics. It is widely believed that the system-bath heat exchange obeys the famous Jarzynski-Wójcik fluctuation theorem. However, this theorem is established in the Born-Markovian approximation under the weak-coupling condition. Via studying the energy exchange between a harmonic oscillator and its coupled bath in the non-Markovian dynamics, we establish a generalized quantum fluctuation theorem for energy exchange being valid for arbitrary coupling strength. The Jarzynski-Wójcik fluctuation theorem is recovered in the weak-coupling limit. We also find the average energy exchange exhibits rich nonequilibrium characteristics when different numbers of system-bath bound states are formed, which suggests a useful way to control the quantum heat. Deepening our understanding of the fluctuation relation in quantum thermodynamics, our result lays the foundation to design high-efficiency quantum heat engines.

arXiv:2401.15533•Physical Review Letters•Jul 30, 2024•10 citations

Stochastic thermodynamics of a finite quantum system coupled to a heat bath

Heinz–Jürgen Schmidt, Jürgen Schnack, Jochen Gemmer

Abstract We consider a situation where an N-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation, we derive general Jarzynski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.

arXiv:2104.05350•Zeitschrift für Naturforschung A•Jun 19, 2021•3 citations

Fluctuation relation for quantum heat engines and refrigerators

Michele Campisi

At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoirs of temperatures T C ⩽ T H can outperform the ideal Carnot engine: 〈 W 〉/〈 Q H 〉 ⩽ 1 − T C / T H . This inequality follows from an exact fluctuation relation involving the nonequilibrium work W and heat exchanged with the hot bath Q H . In a previous work (Sinitsyn 2011 J. Phys. A: Math. Theor. 44 405001) this fluctuation relation was obtained under the assumption that the heat engine undergoes a stochastic jump process. Here we provide the general quantum derivation, and also extend it to the case of refrigerators, in which case Carnot's statement reads 〈 Q C 〉/|〈 W 〉| ⩽ ( T H / T C − 1) −1 .

arXiv:1403.8040•Journal of Physics A Mathematical and Theoretical•Jun 2, 2014•86 citations

Quantum heat-fluctuation theorem of a reduced system: An exactly solvable case

Zhan-Wu Bai

For a system in which free quantum Brownian particles interact with a non-Markovian heat bath with product initial states, the quantum heat-fluctuation theorems and the Jarzynski relation of the reduced system are derived using the path integral technique. They are not a direct generalization of the classical case. The validity of the second law of quantum thermodynamics is shown. The forms of these theorems and relations have to do with the specified nonequilibrium initial states, and are dependent on the structure of the bath (ergodic or nonergodic) in the quantum case as well as the classical case under some initial states.

Physical Review E•Feb 2, 2011•0 citations
A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. Interestingly, this relation is akin to the standard form of the fluctuation relation (for forward-backward dynamics). We also argue that the probability of the violation of the second law of thermodynamics in the form of the Clausius statement (i.e., net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences of the baths.
The quantum exchange fluctuation theorem relates the probabilities of observing heat transfer along and against the temperature gradient between thermal baths at different temperatures. We investigate how this relation generalizes when the baths exhibit non-Markovian dynamics. Using a microscopic collisional model, bath memory is generated through interactions between successive bath auxiliaries before each heat-exchange collision. We derive exchange fluctuation theorems for both direct bath-bath interactions and probe-mediated heat exchange in the steady-state regime. As an illustrative example, we consider heat baths with qubit auxiliaries and show that non-Markovian memory enhances the probability of heat-transfer events against the temperature gradient, modifying the predictions made by the conventional Jarzynski-Wójcik exchange fluctuation theorem. Our results establish a microscopic connection between environmental memory and non-equilibrium heat-exchange statistics.
We consider a situation where an NNN-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general Jarzinski-type equation and conclude that heat and entropy is flowing from the hot bath to the cold one. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities. Our approach is illustrated by an analytical example. For the linear regime, i.~e., for small temperature differences between the two heat baths we derive an expression for the heat conduction coefficient.
The nonequilibrium fluctuation relation is a cornerstone of quantum thermodynamics. It is widely believed that the system-bath heat exchange obeys the famous Jarzynski-Wójcik fluctuation theorem. However, this theorem is established in the Born-Markovian approximation under the weak-coupling condition. Via studying the energy exchange between a harmonic oscillator and its coupled bath in the non-Markovian dynamics, we establish a generalized quantum fluctuation theorem for energy exchange being valid for arbitrary coupling strength. The Jarzynski-Wójcik fluctuation theorem is recovered in the weak-coupling limit. We also find the average energy exchange exhibits rich nonequilibrium characteristics when different numbers of system-bath bound states are formed, which suggests a useful way to control the quantum heat. Deepening our understanding of the fluctuation relation in quantum thermodynamics, our result lays the foundation to design high-efficiency quantum heat engines.
Abstract We consider a situation where an N-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation, we derive general Jarzynski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.
At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoirs of temperatures T C ⩽ T H can outperform the ideal Carnot engine: 〈 W 〉/〈 Q H 〉 ⩽ 1 − T C / T H . This inequality follows from an exact fluctuation relation involving the nonequilibrium work W and heat exchanged with the hot bath Q H . In a previous work (Sinitsyn 2011 J. Phys. A: Math. Theor. 44 405001) this fluctuation relation was obtained under the assumption that the heat engine undergoes a stochastic jump process. Here we provide the general quantum derivation, and also extend it to the case of refrigerators, in which case Carnot's statement reads 〈 Q C 〉/|〈 W 〉| ⩽ ( T H / T C − 1) −1 .
For a system in which free quantum Brownian particles interact with a non-Markovian heat bath with product initial states, the quantum heat-fluctuation theorems and the Jarzynski relation of the reduced system are derived using the path integral technique. They are not a direct generalization of the classical case. The validity of the second law of quantum thermodynamics is shown. The forms of these theorems and relations have to do with the specified nonequilibrium initial states, and are dependent on the structure of the bath (ergodic or nonergodic) in the quantum case as well as the classical case under some initial states.