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:1704.00574 · Physical review. B./Physical review. B

Nonequilibrium thermodynamics of continuously measured quantum systems: A circuit QED implementation

P. G. Di Stefano, Jose Joaquin Alonso, Eric Lutz, G. Falci, Mauro Paternostro

Published Oct 17, 2018• 18 citations
arXivHTMLPDF

Abstract

We propose an operational framework to study the nonequilibrium thermodynamics of a quantum system $S$ that is coupled to a detector $D$ whose state is continuously monitored, allowing us to single out individual quantum trajectories of $S$. We focus on detailed fluctuation theorems and characterize the entropy production of the system. We establish fundamental differences with respect to the thermodynamics of unmonitored, unitarily evolved systems. We consider the paradigmatic example of circuit QED, where superconducting qubits can be coupled to a continuously monitored resonator and show numerical simulations using state-of-the-art experimental parameters.

DOI
10.1103/physrevb.98.144514

Related papers

Quantum thermodynamics under continuous monitoring: A general framework

Gonzalo Manzano, Roberta Zambrini

The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Here, we provide an introduction to the general theoretical framework to establish and interpret the thermodynamics for quantum systems whose nonequilibrium evolution is continuously monitored. We review the formalism of quantum trajectories and its consistent application to the thermodynamic scenario, where primary quantities such as work, heat, and entropy production can be defined at the stochastic level. The connection to irreversibility and fluctuation theorems is also discussed together with some recent developments, and we provide some simple examples to illustrate the general theoretical framework.

arXiv:2112.02019•AVS Quantum Science•May 31, 2022•61 citations

Entropy production in continuously measured Gaussian quantum systems

Alessio Belenchia, Luca Mancino, Gabriel Teixeira Landi +1 more

Abstract The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.

arXiv:1908.09382•npj Quantum Information•Dec 4, 2020•39 citations

Thermodynamics of Monitored Non-Markovian Quantum Systems

LUDOVICO LENZUNI

We study the thermalization dynamics and thermodynamics of a qubit coupled to a structured, memory-carrying environment modeled as a single bosonic mode continuously thermalized by a Markovian bath. The competition between coherent qubit-mode coupling g and thermalization rate κ is controlled by the dimensionless ratio μ=g/κ, which drives a crossover between Markovian and strongly non-Markovian regimes. In the strongly non-Markovian limit, coherent energy exchange produces transient shortcuts to local thermalization, whereby the qubit approaches its thermal state long before global equilibration. In the opposite limit, we derive an original convolution master equation with an exponential memory kernel, which reduces to a thermal GKSL equation as μ→0. The crossover between the two regimes closely mirrors the underdamped-to-overdamped transition of a classical damped oscillator. From the thermodynamic side, we derive an original decomposition of the reduced entropy production in terms of qubit-ancilla mutual information and ancilla relative entropy, providing a quantitative fingerprint of non-Markovian corrections. We then extend this framework to the stochastic level via two monitoring protocols — Fock-state tracking and energy-exchange detection — constructing trajectory-level entropy productions and establishing fluctuation theorems tailored to each scheme. Together, these results demonstrate that a self-consistent stochastic thermodynamics can be formulated for non-Markovian open quantum systems under continuous monitoring.

•Jul 15, 2026•0 citations

Continuously monitored quantum systems beyond Lindblad dynamics

Guglielmo Lami, Alessandro Santini, Mario Collura

Abstract The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterizes expectation values, the entire ensemble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.

arXiv:2305.04108•New Journal of Physics•Jan 16, 2024•6 citations

Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection

Mar Ferri-Cortés, José A. Almanza-Marrero, Rosa López +2 more

The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the definition of main thermodynamic quantities becomes subtle and universal fluctuation relations are unknown. Here, we fill this gap by deriving a universal fluctuation relation that links thermodynamic entropy production and information-theoretical irreversibility along single trajectories in inefficient monitoring setups. This relation provides as a corollary an irreversibility estimator of dissipation using imperfect detection records that lower bounds the underlying entropy production at the level of visible trajectories. We illustrate our findings with a driven-dissipative two-level system following quantum jump trajectories and discuss the experimental applicability of our results for thermodynamic inference.

arXiv:2308.08491•Physical Review Research•Jan 21, 2025•10 citations

Quantum Fluctuation Theorems for Arbitrary Environments: Adiabatic and Nonadiabatic Entropy Production

Gonzalo Manzano, Jordan M. Horowitz, Juan M. R. Parrondo

We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments.First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics.Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin.We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.

arXiv:1710.00054•Physical Review X•Aug 6, 2018•154 citations
We propose an operational framework to study the nonequilibrium thermodynamics of a quantum system SSS that is coupled to a detector DDD whose state is continuously monitored, allowing us to single out individual quantum trajectories of SSS. We focus on detailed fluctuation theorems and characterize the entropy production of the system. We establish fundamental differences with respect to the thermodynamics of unmonitored, unitarily evolved systems. We consider the paradigmatic example of circuit QED, where superconducting qubits can be coupled to a continuously monitored resonator and show numerical simulations using state-of-the-art experimental parameters.
The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Here, we provide an introduction to the general theoretical framework to establish and interpret the thermodynamics for quantum systems whose nonequilibrium evolution is continuously monitored. We review the formalism of quantum trajectories and its consistent application to the thermodynamic scenario, where primary quantities such as work, heat, and entropy production can be defined at the stochastic level. The connection to irreversibility and fluctuation theorems is also discussed together with some recent developments, and we provide some simple examples to illustrate the general theoretical framework.
Abstract The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.
We study the thermalization dynamics and thermodynamics of a qubit coupled to a structured, memory-carrying environment modeled as a single bosonic mode continuously thermalized by a Markovian bath. The competition between coherent qubit-mode coupling g and thermalization rate κ is controlled by the dimensionless ratio μ=g/κ, which drives a crossover between Markovian and strongly non-Markovian regimes. In the strongly non-Markovian limit, coherent energy exchange produces transient shortcuts to local thermalization, whereby the qubit approaches its thermal state long before global equilibration. In the opposite limit, we derive an original convolution master equation with an exponential memory kernel, which reduces to a thermal GKSL equation as μ→0. The crossover between the two regimes closely mirrors the underdamped-to-overdamped transition of a classical damped oscillator. From the thermodynamic side, we derive an original decomposition of the reduced entropy production in terms of qubit-ancilla mutual information and ancilla relative entropy, providing a quantitative fingerprint of non-Markovian corrections. We then extend this framework to the stochastic level via two monitoring protocols — Fock-state tracking and energy-exchange detection — constructing trajectory-level entropy productions and establishing fluctuation theorems tailored to each scheme. Together, these results demonstrate that a self-consistent stochastic thermodynamics can be formulated for non-Markovian open quantum systems under continuous monitoring.
Abstract The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterizes expectation values, the entire ensemble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.
The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the definition of main thermodynamic quantities becomes subtle and universal fluctuation relations are unknown. Here, we fill this gap by deriving a universal fluctuation relation that links thermodynamic entropy production and information-theoretical irreversibility along single trajectories in inefficient monitoring setups. This relation provides as a corollary an irreversibility estimator of dissipation using imperfect detection records that lower bounds the underlying entropy production at the level of visible trajectories. We illustrate our findings with a driven-dissipative two-level system following quantum jump trajectories and discuss the experimental applicability of our results for thermodynamic inference.
We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments.First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics.Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin.We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.