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.
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.
This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schrödinger equation allows to construct quantum trajectories describing the dynamics of the system state vector in presence of an eventually monitored environment. Thermodynamic quantities are defined at the single quantum trajectory level, independently of any energy measurement, at any time of the protocol. We thereby identify coherent contributions, without classical counterparts, leading to quantum fluctuations of thermodynamic quantities. This formalism eventually leads to central fluctuation theorems for entropy, extending in the quantum regime results obtained in classical stochastic thermodynamics. The thermal imprint of coherences on a simple implementation of Jarzynski equality is investigated, opening avenues for a thermodynamic approach to decoherence.
We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on noninteracting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.
We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the l1-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.
Abstract Non-Markovian dynamics is central to quantum information processing, as memory effects strongly influence coherence preservation, metrology, and communication. In this work, we investigate the role of stochastic system–bath couplings in shaping non-Markovian behavior of open quantum systems, using the central spin model within a time-convolutionless master equation framework. We show that the character of the reduced dynamics depends jointly on the intrinsic memory of the environment and on the structure of the system–environment interaction. In certain regimes, the dynamics simplify to pure dephasing, while in general both amplitude damping and dephasing contribute to the evolution. By employing two complementary measures: the Quantum Fisher Information (QFI) flow and the Breuer–Laine–Piilo (BLP) measure, we demonstrate that QFI flow may fail to witness memory effects in weak-coupling and near-resonant regimes, whereas the BLP measure still detects information backflow. Furthermore, external modulation of the interaction kernel produces qualitatively richer behavior, including irregular and frequency-dependent revivals of non-Markovianity. These results clarify the physical origin of memory effects, highlight the limitations of single-witness approaches, and suggest that stochasticity and modulation can be harnessed to engineer robust, noise-resilient quantum technologies.
Quantum systems are inherently open to their environment and thus they evolve under the influence of dissipation, decoherence and driving from external fields. This poses a significant theoretical challenge: how to track the dynamics of the system of interest while tracing out environmental degrees of freedom. Markovian master equations offer a longstanding solution to this problem, where under a series of assumptions the reduced density matrix of the system can be obtained. These flexible approaches provide a conceptually and numerically simple framework for describing complex many-body systems. However, the assumptions enforced by Markovian master equations create a gap in the availability of generic, simple, and analytical techniques capable of treating open quantum systems beyond the regimes of standard Markovian master equations. In this thesis, we introduce three studies addressing three regimes that are inaccessible to standard Markovian master equations and investigate their consequences in quantum thermodynamics-inspired applications. We begin by developing a Markovian embedding technique to tackle non-Markovian dynamics induced by the long correlation times of a qubit coupled to a structured environment. Subsequently, we propose an "effective" Hamiltonian theory enabling the study of equilibrium properties of strong coupling to a thermal reservoir through a dressed version of the Gibbs state. This framework can also be applied to address problems of equilibration, transport, quantum thermal machines, and quantum dynamics. Lastly, we showcase the importance of including non-secular terms in the quantum master equation, which results in a drastic separation of timescales leading to rich metastable dynamics. We apply this quantum master equation approach to temperature sensing in a nonequilibrium setting offering an alternative to standard equilibrium probes. Overall, this thesis contributes novel theoretical techniques for tackling open quantum systems beyond standard approximations with applications in quantum thermodynamics.
Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback control is expected to further suppress fluctuations, its role within the TUR framework has remained unclear, particularly in quantum systems where control is inherently information-driven. In this Letter, we consider open quantum systems weakly coupled to a thermal environment, in which quantum jumps are continuously monitored, and Markovian feedback is applied. Using quantum mutual information to quantify the information contribution induced by feedback, we derive a finite-time TUR for arbitrary time-integrated currents in terms of entropy production and mutual information. Our results uncover how feedback control suppresses fluctuations together with thermodynamic cost and establish a fundamental precision bound imposed by information-based control. As an application, we analyze a quantum clock model and demonstrate that the clock precision can be enhanced by feedback control in the presence of a single thermal reservoir.