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:2301.13544 · Journal of Statistical Mechanics Theory and Experiment

Heat currents in qubit systems

Hans C. Fogedby

Published Jul 23, 2024• 0 citations
arXivHTMLPDF

Abstract

Abstract There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e. the flow of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been on composite system and in particular the issue regarding the application of local or global master equations. In order to contribute to this discussion we discuss two cases, namely as an example a single qubit and as a simple composite system two coupled qubits driven by two heat reservoirs at different temperatures, respectively. Applying a global Lindblad master equation approach we present explicit expressions for the heat currents in agreement with the second law of thermodynamics. The analysis is carried out in the Born–Markov approximation. We also discuss issues regarding the possible presence of coherences in the steady state.

DOI
10.1088/1742-5468/ad5c5b

Related papers

Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation

Marco Cattaneo, Gian Luca Giorgi, Sabrina Maniscalco +1 more

Abstract Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.

arXiv:1906.08893•New Journal of Physics•Nov 1, 2019•168 citations

Quantum thermodynamically consistent local master equations

Adam Hewgill, Gabriele De Chiara, Alberto Imparato

Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems.These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics.In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works.In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents, and entropy production rate.We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents.We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics.We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier.For the machines considered here, we also perform an optimization of the system parameters using an algorithm of reinforcement learning.

arXiv:2008.04742•Physical Review Research•Feb 19, 2021•61 citations

Periodically driven quantum open systems: Tutorial

Robert Alicki, David Gelbwaser-Klimovsky, Gershon Kurizki

We present a short derivation and discussion of the master equation for an open quantum system weakly coupled to a heat bath and then its generalization to the case of with periodic external driving based on the Floquet theory. Further, a single heat bath is replaced by several ones. We present also the definition of heat currents which satisfies the second law of thermodynamics and apply the general results to a simple model of periodically modulated qubit.

arXiv:1205.4552•May 21, 2012•18 citations

Reconciliation of quantum local master equations with thermodynamics

Gabriele De Chiara, Gabriel Teixeira Landi, Adam Hewgill +4 more

The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics.

arXiv:1808.10450•New Journal of Physics•Oct 31, 2018•250 citations

Quantum Master Equations for Composite Systems: Is Born–Markov Approximation Really Valid?

Masatoshi Nakatani, Tetsuo Ogawa

Markovian quantum master equations are generally thought to satisfy the following three conditions: (i) they describe the dynamics of time scales that are larger than the reservoir correlation time scale, (ii) these stationary solutions give the thermal equilibrium states with a reservoir, and (iii) they can be written in the Lindblad form. In fact, for single systems such as a single harmonic oscillator and a single two-level system, Markovian quantum master equations satisfying all these conditions can be obtained. However, for composite systems, which consist of more than one subsystem coupled with each other, such equations have not been obtained thus far. In this study, we found that we cannot use the Born–Markov approximation for obtaining quantum master equations for composite systems in the strong-coupling regime, no matter how short the reservoir correlation time is.

Journal of the Physical Society of Japan•Aug 10, 2010•22 citations

Thermodynamics of a qubit undergoing dephasing

Stefano Marcantoni

The thermodynamics of a qubit undergoing dephasing due to the coupling with the external environment is discussed. First of all, we assume the dynamics of the system to be described by a master equation in Lindblad form. In this framework, we review a standard formulation of the first and second law of thermodynamics that has been known in literature for a long time. After that, we explicitly model the environment with a set of quantum harmonic oscillators choosing the interaction such that the global dynamics of system and bath is analytically solvable and the Lindblad master equation is recovered in the weak-coupling limit. In this generalized setting, we can show that the correlations between system and bath play a fundamental role in the heat exchange. Moreover, the internal entropy production of the qubit is proven to be positive for arbitrary coupling strength.

Journal of Physics Conference Series•May 1, 2017•4 citations
Abstract There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e. the flow of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been on composite system and in particular the issue regarding the application of local or global master equations. In order to contribute to this discussion we discuss two cases, namely as an example a single qubit and as a simple composite system two coupled qubits driven by two heat reservoirs at different temperatures, respectively. Applying a global Lindblad master equation approach we present explicit expressions for the heat currents in agreement with the second law of thermodynamics. The analysis is carried out in the Born–Markov approximation. We also discuss issues regarding the possible presence of coherences in the steady state.
Abstract Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems.These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics.In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works.In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents, and entropy production rate.We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents.We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics.We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier.For the machines considered here, we also perform an optimization of the system parameters using an algorithm of reinforcement learning.
The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics.
Markovian quantum master equations are generally thought to satisfy the following three conditions: (i) they describe the dynamics of time scales that are larger than the reservoir correlation time scale, (ii) these stationary solutions give the thermal equilibrium states with a reservoir, and (iii) they can be written in the Lindblad form. In fact, for single systems such as a single harmonic oscillator and a single two-level system, Markovian quantum master equations satisfying all these conditions can be obtained. However, for composite systems, which consist of more than one subsystem coupled with each other, such equations have not been obtained thus far. In this study, we found that we cannot use the Born–Markov approximation for obtaining quantum master equations for composite systems in the strong-coupling regime, no matter how short the reservoir correlation time is.
The thermodynamics of a qubit undergoing dephasing due to the coupling with the external environment is discussed. First of all, we assume the dynamics of the system to be described by a master equation in Lindblad form. In this framework, we review a standard formulation of the first and second law of thermodynamics that has been known in literature for a long time. After that, we explicitly model the environment with a set of quantum harmonic oscillators choosing the interaction such that the global dynamics of system and bath is analytically solvable and the Lindblad master equation is recovered in the weak-coupling limit. In this generalized setting, we can show that the correlations between system and bath play a fundamental role in the heat exchange. Moreover, the internal entropy production of the qubit is proven to be positive for arbitrary coupling strength.