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:0907.1590 · Journal of Physics A Mathematical and Theoretical

Thermodynamics and fluctuation theorems for a strongly coupled open quantum system: an exactly solvable case

Michele Campisi, Peter Talkner, Peter Hänggi

Published Sep 11, 2009• 52 citations
arXivHTMLPDF

Abstract

We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems [M. Campisi, P. Talkner, and P. Hänggi, Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable model of an open quantum system. The central role played by the thermodynamic partition function of the open quantum system, -- a two level fluctuator with a strong quantum nondemolition coupling to a harmonic oscillator --, is elucidated. The corresponding quantum Hamiltonian of mean force is evaluated explicitly. We study the thermodynamic entropy and the corresponding specific heat of this open system as a function of temperature and coupling strength and show that both may assume negative values at nonzero low temperatures.

DOI
10.1088/1751-8113/42/39/392002

Related papers

Thermodynamics and fluctuation theorems for a strongly coupled open quantum system: an exactly solvable case

Michele Campisi, Peter Talkner A, Peter Hänggi A

We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems (Campisi et al 2009 Phys.Rev. Lett.102 210401), by applying them to a solvable model of an open quantum system.The central role played by the thermodynamic partition function of the open quantum system, a two-level fluctuator with a strong quantum nondemolition coupling to a harmonic oscillator, is elucidated.The corresponding quantum Hamiltonian of mean force is evaluated explicitly.We study the thermodynamic entropy and the corresponding specific heat of this open system as a function of temperature and coupling strength and show that both may assume negative values at nonzero low temperatures.

•Jan 1, 2009•53 citations

Nonequilibrium Entropy Production for Open Quantum Systems

Sebastian Deffner, Eric Lutz

We consider open quantum systems weakly coupled to a heat reservoir and driven by arbitrary time-dependent parameters. We derive exact microscopic expressions for the nonequilibrium entropy production and entropy production rate, valid arbitrarily far from equilibrium. By using the two-point energy measurement statistics for system and reservoir, we further obtain a quantum generalization of the integrated fluctuation theorem put forward by Seifert [Phys. Rev. Lett. 95, 040602 (2005)].

arXiv:1103.4775•Physical Review Letters•Sep 30, 2011•225 citations

Fluctuation Theorem for Information Thermodynamics of Quantum Correlated Systems

Jung Jun Park, Hyunchul Nha

We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems.

Entropy•Jan 13, 2023•5 citations

Thermodynamics of quantum Brownian motion with internal degrees of freedom: the role of entanglement in the strong-coupling quantum regime

Christian Hörhammer, H. Büttner

We study the influence of entanglement on the relation between the statistical entropy of an open quantum system and the heat exchanged with a low temperature environment. A model of quantum Brownian motion of the Caldeira–Leggett type—for which a violation of the Clausius inequality has been stated by Th M Nieuwenhuizen and A E Allahverdyan (2002 Phys. Rev. E 66 036102)—is re-examined and the results of the cited work are put into perspective. In order to address the problem from an information theoretical viewpoint a model of two coupled Brownian oscillators is formulated that can also be viewed as a continuum version of a two-qubit system. The influence of an additional internal coupling parameter on heat and entropy changes is described and the findings are compared to the case of a single Brownian particle.

arXiv:cond-mat/0408536•Journal of Physics A Mathematical and General•Aug 3, 2005•24 citations

Fluctuations of path-dependent thermodynamic quantities in open quantum systems via two-point system-only measurements

Alessandra Colla, Andrea Smirne, Heinz-Peter Breuer +1 more

We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat, and to isolate correction factors to Jarzynski's equality, requiring only access to the system degrees of freedom. This framework is flexible and can be applied to the limiting case of closed systems, recovering previous, yet seemingly contradictory, results from the literature. Moreover, the formalism admits a straightforward extension to strongly coupled open quantum systems. We investigate the effect of specific dynamical classes on the fluctuation relations, and show that the pure decoherence case is particularly special, as it deterministically does not contain any heat contribution and thus constitutes a class of open system dynamics for which the Jarzynski equality for work fluctuations is identically true at any coupling strength. Finally, we look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics, both in the weakly-coupled regime and in the deep non-Markovian regime.

quant-pharXiv:2604.26856•Quantum Science and Technology•Apr 30, 2026•0 citations

The strong-coupling quantum thermodynamics of quantum Brownian motion based on the exact solution of its reduced density matrix

Chuan-Zhe Yao, Wei-Min Zhang

We derive the quantum thermodynamics of quantum Brownian motion from the exact solution of its reduced density matrix. We start from the total equilibrium thermal state between the Brownian particle and its reservoir, and solve analytically and exactly the reduced density matrix of the system by taking the partial trace over all the reservoir states. We find that the reduced Hamiltonian and the reduced partition function of the Brownian motion must be renormalized significantly, as shown in the general nonperturbative renormalization theory of quantum thermodynamics for open quantum systems we developed recently [Phys. Rev. Res. 4, 023141 (2022)]. The reduced Hamiltonian contains not only a frequency shift but also a squeezing pairing interaction, where a momentum-dependent potential is generated naturally from the strong coupling between the Brownian particle and the reservoir, after traced over all the reservoir states. The resulting exact reduced density matrix of the Brownian motion is given by a squeezing thermal state. Moreover, beyond the weak coupling limit, in order to obtain correctly the reduced partition function of the Brownian motion, one must take into account the non-negligible changes of the reservoir state induced by the system-reservoir coupling. Using the exact solutions of the reduced density matrix, the reduced Hamiltonian as well as the reduced partition function of the Brownian motion, we show that the controversial results obtained from the different definitions of internal energy and the issue of the negative heat capacity in the previous studies of strong-coupling quantum thermodynamics are resolved.

arXiv:2405.00277•May 1, 2024•0 citations
We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems [M. Campisi, P. Talkner, and P. Hänggi, Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable model of an open quantum system. The central role played by the thermodynamic partition function of the open quantum system, -- a two level fluctuator with a strong quantum nondemolition coupling to a harmonic oscillator --, is elucidated. The corresponding quantum Hamiltonian of mean force is evaluated explicitly. We study the thermodynamic entropy and the corresponding specific heat of this open system as a function of temperature and coupling strength and show that both may assume negative values at nonzero low temperatures.
We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems (Campisi et al 2009 Phys.Rev. Lett.102 210401), by applying them to a solvable model of an open quantum system.The central role played by the thermodynamic partition function of the open quantum system, a two-level fluctuator with a strong quantum nondemolition coupling to a harmonic oscillator, is elucidated.The corresponding quantum Hamiltonian of mean force is evaluated explicitly.We study the thermodynamic entropy and the corresponding specific heat of this open system as a function of temperature and coupling strength and show that both may assume negative values at nonzero low temperatures.
We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems.
We study the influence of entanglement on the relation between the statistical entropy of an open quantum system and the heat exchanged with a low temperature environment. A model of quantum Brownian motion of the Caldeira–Leggett type—for which a violation of the Clausius inequality has been stated by Th M Nieuwenhuizen and A E Allahverdyan (2002 Phys. Rev. E 66 036102)—is re-examined and the results of the cited work are put into perspective. In order to address the problem from an information theoretical viewpoint a model of two coupled Brownian oscillators is formulated that can also be viewed as a continuum version of a two-qubit system. The influence of an additional internal coupling parameter on heat and entropy changes is described and the findings are compared to the case of a single Brownian particle.
We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat, and to isolate correction factors to Jarzynski's equality, requiring only access to the system degrees of freedom. This framework is flexible and can be applied to the limiting case of closed systems, recovering previous, yet seemingly contradictory, results from the literature. Moreover, the formalism admits a straightforward extension to strongly coupled open quantum systems. We investigate the effect of specific dynamical classes on the fluctuation relations, and show that the pure decoherence case is particularly special, as it deterministically does not contain any heat contribution and thus constitutes a class of open system dynamics for which the Jarzynski equality for work fluctuations is identically true at any coupling strength. Finally, we look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics, both in the weakly-coupled regime and in the deep non-Markovian regime.
We derive the quantum thermodynamics of quantum Brownian motion from the exact solution of its reduced density matrix. We start from the total equilibrium thermal state between the Brownian particle and its reservoir, and solve analytically and exactly the reduced density matrix of the system by taking the partial trace over all the reservoir states. We find that the reduced Hamiltonian and the reduced partition function of the Brownian motion must be renormalized significantly, as shown in the general nonperturbative renormalization theory of quantum thermodynamics for open quantum systems we developed recently [Phys. Rev. Res. 4, 023141 (2022)]. The reduced Hamiltonian contains not only a frequency shift but also a squeezing pairing interaction, where a momentum-dependent potential is generated naturally from the strong coupling between the Brownian particle and the reservoir, after traced over all the reservoir states. The resulting exact reduced density matrix of the Brownian motion is given by a squeezing thermal state. Moreover, beyond the weak coupling limit, in order to obtain correctly the reduced partition function of the Brownian motion, one must take into account the non-negligible changes of the reservoir state induced by the system-reservoir coupling. Using the exact solutions of the reduced density matrix, the reduced Hamiltonian as well as the reduced partition function of the Brownian motion, we show that the controversial results obtained from the different definitions of internal energy and the issue of the negative heat capacity in the previous studies of strong-coupling quantum thermodynamics are resolved.