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Journal of Physics A Mathematical and Theoretical

Stochastic resetting as a non-Markovian eraser in a quantum Otto heat engine

Chun-Hui 春辉 Wang 王, Haoran Hu

Published Aug 18, 2026• 0 citations
Publisher

Abstract

Abstract We investigate the thermodynamic performance of a quantum Otto heat engine modulated by stochastic resetting, utilizing an exact discrete-time collision framework of a qubit coupled to a hierarchical non-Markovian environment. By evaluating the exact ensemble-averaged dynamics, we demonstrate that state-selective resetting functions as a targeted ‘non-Markovian eraser’ that repeatedly severs instantaneous system–memory correlations. Consequently, resetting dramatically dampens persistent, memory-induced heat-flux oscillations in strong-memory regimes, whereas its impact on effectively Markovian relaxation remains virtually negligible owing to the intrinsically weak environmental memory effects in this regime. By implementing an optimal stroke-dependent resetting protocol, the work extraction is monotonically maximized, displaying an approximately linear scaling in the effectively Markovian regime and a pronounced nonlinear boost under strong memory effects. Crucially, the effective efficiency remains close to the conventional Otto benchmark within numerical accuracy under effectively Markovian dynamics, whereas in the non-Markovian regime it increases monotonically with the resetting rate by actively erasing parasitic, memory-induced heat absorption. This work establishes state-selective resetting as a potent control strategy for managing environmental memory and optimizing nonequilibrium quantum thermal machines in complex open systems.

DOI
10.1088/1751-8121/ae9b4e

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•Jan 1, 2019•0 citations
Abstract We investigate the thermodynamic performance of a quantum Otto heat engine modulated by stochastic resetting, utilizing an exact discrete-time collision framework of a qubit coupled to a hierarchical non-Markovian environment. By evaluating the exact ensemble-averaged dynamics, we demonstrate that state-selective resetting functions as a targeted ‘non-Markovian eraser’ that repeatedly severs instantaneous system–memory correlations. Consequently, resetting dramatically dampens persistent, memory-induced heat-flux oscillations in strong-memory regimes, whereas its impact on effectively Markovian relaxation remains virtually negligible owing to the intrinsically weak environmental memory effects in this regime. By implementing an optimal stroke-dependent resetting protocol, the work extraction is monotonically maximized, displaying an approximately linear scaling in the effectively Markovian regime and a pronounced nonlinear boost under strong memory effects. Crucially, the effective efficiency remains close to the conventional Otto benchmark within numerical accuracy under effectively Markovian dynamics, whereas in the non-Markovian regime it increases monotonically with the resetting rate by actively erasing parasitic, memory-induced heat absorption. This work establishes state-selective resetting as a potent control strategy for managing environmental memory and optimizing nonequilibrium quantum thermal machines in complex open systems.
Abstract We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution time, and the memory-bearing character of the system-environment evolution.
It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well-known single-qubit Otto engine; the non-Markovian behavior is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a single qubit rotation. It is shown that the non-Markovian Otto engine can generate more work-per-cycle for a given efficiency than its Markovian counterpart, whereas performance of both setups is superior to the three-stroke engine. Furthermore, both the non-Markovian Otto engine and the three-stroke engine can reduce the work fluctuations in comparison with the Markovian Otto engine, with their relative advantage depending on the performance target. This demonstrates the beneficial influence of non-Markovianity on both the average performance and the stability of operation of quantum heat engines.
Stochastic resetting describes dynamics which are reinitialized to a reference state at random times. These protocols are attracting significant interest: they can stabilize nonequilibrium stationary states, generate correlations in noninteracting systems, and enable optimal search strategies. While a constant reset probability results in a Markovian dynamics, much less is known about non-Markovian effects in quantum stochastic resetting. Here, we analyze memory effects in these processes -- examining the evolution of quantum states and of observables -- through witnesses of non-Markovianity for open quantum systems. We focus on discrete-time reset processes, which are of particular interest as they can be implemented on existing gate-operated quantum devices. We show that these processes are generically described by non-divisible maps and, in non-classical scenarios where the effective reset probability can become negative, can feature revivals in the state distinguishability. Our results reveal non-Markovian effects in quantum stochastic resetting and show that a time-dependent reset may be exploited to engineer enhanced stationary quantum correlations.
Abstract Real quantum heat engines lack the separation of time and length scales that is characteristic for classical engines. They must be understood as open quantum systems in non-equilibrium with time-controlled coupling to thermal reservoirs as integral part. Here, we present a systematic approach to describe a broad class of engines and protocols beyond conventional weak coupling treatments starting from a microscopic modeling. For the four stroke Otto engine the full dynamical range down to low temperatures is explored and the crucial role of the work associated with the coupling/de-coupling to/from reservoirs as an integral part in the energy balance is revealed. Quantum correlations turn out to be instrumental to enhance the efficiency which opens new ways for optimal control techniques.
We develop an exact theory of coherence-selective stroboscopic resetting for quadratic open quantum systems within the single-particle density-matrix formalism. We focus on the survival of coherences and the associated thermodynamic cost at the stroboscopic fixed point. To this end, we introduce a one-parameter family of reset channels that continuously interpolates between complete coherence erasure and complete coherence preservation. This unifies the reset-map description, the repeated-interaction and evolving-correlation endpoint channels, and the thermodynamic cost of environmental reinitialization. For a single fermionic level coupled to a structured semi-infinite tight-binding bath, we derive the exact affine stroboscopic map, solve for its unique fixed point, and compute the retained coherence spectrum, the post-reset occupation, and the reset heat current. We find that retained coherence increases monotonically with the retention parameter, whereas the reset heat current is generically nonmonotonic and is maximized at an intermediate operating point. Thus the protocol that stores the most coherence is not the one that dissipates the most heat. Exact operating diagrams further show that coherence-optimal and coherence-per-cost-optimal protocols are both driven toward the coherence-preserving endpoint, while the heat-optimal protocol depends strongly on the reset interval. We also show that this coherence-cost geometry survives at nonzero chemical potential as a filling-biased deformation of the same fixed-point tradeoff, rather than as an independent particle-current optimization problem. These results establish coherence-selective resetting as a distinct control principle for structured-bath open quantum systems and provide an exactly solvable benchmark for memory engineering and thermodynamic optimization under repeated environmental reinitialization.
This cumulative thesis presents new advances in the field of non-Markovian dynamics of open quantum systems based on the formally exact and non-perturbative stochastic Liouville-von Neumann (SLN) framework. More specifically, it presents a general platform to dynamically describe the complete, out-of-equilibrium operation of quantum thermal devices in all temperature and damping ranges and for arbitrary driving frequencies or strengths. Such an approach is urgently required due to the current experimental progress with realizations based on trapped ions, NV-centers in diamond, or superconducting circuits. By providing a comprehensive picture of a quantum Otto engine, the relevance of the thermal coupling work is revealed, an ingredient in the energy balance which has been basically neglected so far and which becomes increasingly relevant in the quantum regime. The thesis further solves crucial issues in dealing with numerical complexity that is inherent to the probabilistic SLN approach in the paradigmatic case of discrete few-level systems in contact with an Ohmic environment. It provides numerically exact benchmark data which is needed to generalize a related, numerically efficient technique for heat transport across open quantum chains to nonlinear systems that show rectification.