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:1711.07139 · Frontiers of Physics

Fluctuation relations for heat exchange in the generalized Gibbs ensemble

Bo-Bo Wei

Published Sep 12, 2018• 0 citations
arXivHTMLPDF

Abstract

In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wójcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at various generalized temperatures. Secondly, we extend the connections between heat exchange and the Rényi divergences to quantum systems under generic initial conditions. These relations are applicable for quantum systems with conserved quantities and universally valid for quantum systems in the integrable and chaotic regimes.

DOI
10.1007/s11467-018-0822-y

Related papers

Relations between dissipated work and Rényi divergences in the generalized Gibbs ensemble

Bo-Bo Wei

In this work, we show that the dissipation in a many-body system under an arbitrary nonequilibrium process is related to the R\'enyi divergences between two states along the forward and reversed dynamics under a very general family of initial conditions. This relation generalizes the links between dissipated work and R\'enyi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model and the Jaynes-Cummings model which are driven out of equilibrium.

arXiv:1711.03855•Physical Review A•Apr 30, 2018•6 citations

Heat exchange and fluctuation in Gaussian thermal states in the quantum realm

A. R. Usha Devi, Sudha, A. K. Rajagopal +1 more

Abstract The celebrated exchange fluctuation theorem—proposed by Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) for heat exchange between two systems in thermal equilibrium at different temperatures—is explored here for quantum Gaussian states in thermal equilibrium. We employ the Wigner distribution function formalism for quantum states, which exhibits a close resemblance to the classical phase-space trajectory description, to arrive at a formal Jarzynski–Wójcik result. For two Gaussian states in thermal equilibrium at two different temperatures kept in contact with each other for a fixed duration of time, we show that the Jarzynski–Wójcik- like relation reduces to the corresponding classical result in the limit ℏ → 0.

arXiv:2007.04255•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2021•0 citations

Quantum heat fluctuation theorem

P. S. Pal, Sourabh Lahiri, A. M. Jayannavar

Two fundamental ingredients play a decisive role in the foundations of fluctuation relations-the principle of micro-reversibility and the fact that thermal equilibrium is described by Gibbs canonical ensemble. Here we investigate the statistics of heat exchange between quantum finite system coupled to two reservoirs at temperatures Th and Tc in the transient regime. We have obtained an analytical result for quantum heat fluctuation theorem in the transient regime. We consider a composite system consisting of two different heat baths at different temperatures with an intervening medium(system of interest). The system of interest is driven by an external protocol. For our study we invoke von Neumann two point projective measurement in quantum mechanics. Our result is a generalisation of Jarzynski-Wojcik heat fluctuation theorem.

AIP conference proceedings•Jan 1, 2017•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

The Exchange Fluctuation Theorem in Quantum Mechanics

S. Akagawa, N. Hatano

We study the heat transfer between two finite quantum systems initially at different temperatures. We find that a recently proposed fluctuation theorem for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D. K. Wójcik, Phys. Rev. Lett. 92 (2004), 230602], does not generally hold in the presence of a finite heat transfer as in the original form proved for weak coupling. As the coupling is weakened, the deviation from the theorem and the heat transfer vanish in the same order of the coupling. We then discover a condition for the exchange fluctuation theorem to hold in the presence of a finite heat transfer, namely the commutable-coupling condition. We explicitly calculate the deviation from the exchange fluctuation theorem as well as the heat transfer for simple models. We confirm for the models that the deviation indeed has a finite value as far as the coupling between the two systems is finite except for the special point of the commutable-coupling condition. We also confirm analytically that the commutable-coupling condition indeed lets the exchange fluctuation theorem hold exactly under a finite heat transfer.

arXiv:0904.1443•Progress of Theoretical Physics•Jun 1, 2009•5 citations

Fluctuation theorems and the generalized Gibbs ensemble in integrable systems

James M. Hickey, Sam Genway

We derive fluctuation relations for a many-body quantum system prepared in a generalized Gibbs ensemble subject to a general nonequilibrium protocol. By considering isolated integrable systems, we find generalizations to the Tasaki-Crooks and Jarzynski relations. Our approach is illustrated by studying the one-dimensional quantum Ising model subject to a sudden change in the transverse field, where we find that the statistics of the work done and irreversible entropy show signatures of quantum criticality. We discuss these fluctuation relations in the context of thermalization.

arXiv:1403.3542•Physical Review E•Aug 8, 2014•14 citations
In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wójcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at various generalized temperatures. Secondly, we extend the connections between heat exchange and the Rényi divergences to quantum systems under generic initial conditions. These relations are applicable for quantum systems with conserved quantities and universally valid for quantum systems in the integrable and chaotic regimes.
In this work, we show that the dissipation in a many-body system under an arbitrary nonequilibrium process is related to the R\'enyi divergences between two states along the forward and reversed dynamics under a very general family of initial conditions. This relation generalizes the links between dissipated work and R\'enyi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model and the Jaynes-Cummings model which are driven out of equilibrium.
Abstract The celebrated exchange fluctuation theorem—proposed by Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) for heat exchange between two systems in thermal equilibrium at different temperatures—is explored here for quantum Gaussian states in thermal equilibrium. We employ the Wigner distribution function formalism for quantum states, which exhibits a close resemblance to the classical phase-space trajectory description, to arrive at a formal Jarzynski–Wójcik result. For two Gaussian states in thermal equilibrium at two different temperatures kept in contact with each other for a fixed duration of time, we show that the Jarzynski–Wójcik- like relation reduces to the corresponding classical result in the limit ℏ → 0.
Two fundamental ingredients play a decisive role in the foundations of fluctuation relations-the principle of micro-reversibility and the fact that thermal equilibrium is described by Gibbs canonical ensemble. Here we investigate the statistics of heat exchange between quantum finite system coupled to two reservoirs at temperatures Th and Tc in the transient regime. We have obtained an analytical result for quantum heat fluctuation theorem in the transient regime. We consider a composite system consisting of two different heat baths at different temperatures with an intervening medium(system of interest). The system of interest is driven by an external protocol. For our study we invoke von Neumann two point projective measurement in quantum mechanics. Our result is a generalisation of Jarzynski-Wojcik heat fluctuation theorem.
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.
We study the heat transfer between two finite quantum systems initially at different temperatures. We find that a recently proposed fluctuation theorem for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D. K. Wójcik, Phys. Rev. Lett. 92 (2004), 230602], does not generally hold in the presence of a finite heat transfer as in the original form proved for weak coupling. As the coupling is weakened, the deviation from the theorem and the heat transfer vanish in the same order of the coupling. We then discover a condition for the exchange fluctuation theorem to hold in the presence of a finite heat transfer, namely the commutable-coupling condition. We explicitly calculate the deviation from the exchange fluctuation theorem as well as the heat transfer for simple models. We confirm for the models that the deviation indeed has a finite value as far as the coupling between the two systems is finite except for the special point of the commutable-coupling condition. We also confirm analytically that the commutable-coupling condition indeed lets the exchange fluctuation theorem hold exactly under a finite heat transfer.
We derive fluctuation relations for a many-body quantum system prepared in a generalized Gibbs ensemble subject to a general nonequilibrium protocol. By considering isolated integrable systems, we find generalizations to the Tasaki-Crooks and Jarzynski relations. Our approach is illustrated by studying the one-dimensional quantum Ising model subject to a sudden change in the transverse field, where we find that the statistics of the work done and irreversible entropy show signatures of quantum criticality. We discuss these fluctuation relations in the context of thermalization.