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arXiv:2305.10622 · Frontiers in Quantum Science and Technology

Impact of non-Markovian evolution on characterizations of quantum thermodynamics

Devvrat Tiwari, Subhashish Banerjee

Published Jul 5, 2023• 13 citations
arXivHTMLPDF

Abstract

Here, we study the impact of non-Markovian evolution on prominent characteristics of quantum thermodynamics such as ergotropy and power. These are benchmarked by the behavior of the quantum speed limit time. We make use of both geometric-based, particularly the quantum Fisher and Wigner–Yanase information metric, and physical properties-based measures, particularly the relative purity measure and relative entropy of coherence measure, to compute the quantum speed limit time. A simple non-Markovian model of a qubit in a bosonic bath exhibiting non-Markovian amplitude damping evolution is considered, which, from the quantum thermodynamic perspective with finite initial ergotropy, can be envisaged as a quantum battery. To this end, we explore the connections between the physical properties-based measures of the quantum speed limit time and the coherent component of ergotropy. The non-Markovian evolution is shown to impact the recharging process of the quantum battery. Furthermore, a connection between the discharging–charging cycle of the quantum battery and the geometric measures of the quantum speed limit time is observed.

DOI
10.3389/frqst.2023.1207552

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Here, we study the impact of non-Markovian evolution on prominent characteristics of quantum thermodynamics such as ergotropy and power. These are benchmarked by the behavior of the quantum speed limit time. We make use of both geometric-based, particularly the quantum Fisher and Wigner–Yanase information metric, and physical properties-based measures, particularly the relative purity measure and relative entropy of coherence measure, to compute the quantum speed limit time. A simple non-Markovian model of a qubit in a bosonic bath exhibiting non-Markovian amplitude damping evolution is considered, which, from the quantum thermodynamic perspective with finite initial ergotropy, can be envisaged as a quantum battery. To this end, we explore the connections between the physical properties-based measures of the quantum speed limit time and the coherent component of ergotropy. The non-Markovian evolution is shown to impact the recharging process of the quantum battery. Furthermore, a connection between the discharging–charging cycle of the quantum battery and the geometric measures of the quantum speed limit time is observed.
Recently, there has been an upsurge of interest in quantum thermodynamic devices, notably quantum batteries. Quantum batteries serve as energy storage devices governed by the rules of quantum thermodynamics. Here, we propose a model of a quantum battery wherein the system of interest can be envisaged as a battery, and the ambient environment acts as a charger (dissipation) mechanism, modeled along the ubiquitous quantum Brownian motion. We employ quantifiers such as ergotropy and its (in)coherent manifestations, as well as instantaneous and average powers, to characterize the performance of the quantum battery. We investigate the influence of the bath's temperature and the system's coupling with the environment via momentum and position coordinates on the discharging and recharging dynamics. Moreover, we probe the memory effects of the system's dynamics and obtain a relationship between the system's non-Markovian evolution and the battery's recharging process.
Abstract The performance of quantum technologies that use entanglement and coherence as a resource is highly limited by the effects of decoherence due to their interaction with some environment. In particular, it is important to take into account situations where such devices unavoidably interact with surrounding. Here, we study memory effects on energy and ergotropy of quantum batteries in the framework of open system dynamics, where the battery and charger are individually allowed to access a bosonic environment. Our investigation shows that the battery can be fully charged as well as its energy can be preserved for long times in non-Markovian dynamics compared with Markovian dynamics. Moreover, the non-Markovianity increase makes it possible to extract the total stored energy as work and the discharge time becomes longer. Our results indicate that memory effects can play a significant role in improving the performance of quantum batteries.
Abstract We study the effect of non-Markovianity in the charging process of an open-system quantum battery. We employ a collisional model framework, where the environment is described by a discrete set of ancillary systems and memory effects in the dynamics can be introduced by allowing these ancillas to interact. We study in detail the behaviour of the steady-state ergotropy and the impact of the information backflow to the system on the different features characterizing the charging process. Remarkably, we find that there is a maximum value of the ergotropy achievable: this value can be obtained either in the presence of memoryless environment, but only in the large-loss limit, as derived in (Farina et al 2019 Phys. Rev. B 99 035421), or in the presence of an environment with memory also beyond the large-loss limit. In general, we show that the presence of an environment with memory allows us to generate steady-state ergotropy near to its maximum value for a much larger region in the parameter space and thus potentially in a shorter time. Relying on the geometrical measure of non-Markovianity, we show that in both the cases of an environment with and without memory the ergotropy maximum is obtained when the non-Markovianity of the dynamics of the battery is zero, possibly as the result of a non-trivial interplay between the memory effects induced by, respectively, the environment and the charger connected to the battery.
Abstract We investigate non-Markovianity and its effects on thermodynamic principles and quantum battery performance within a structured nonequilibrium environment consisting of a three-level memory unit and two thermal reservoirs. We demonstrate that temperature imbalance, average temperature, and memory structure serve as effective control parameters for modulating non-Markovianity, exhibiting distinct behaviors for bosonic and fermionic reservoirs. An improved Landauer’s bound applicable to non-Markovian processes is derived, overcoming the limitations of its conventional counterpart. By treating the central system as a quantum battery and the environment as a charger, we show that steady-state ergotropy can be achieved and tuned via thermodynamic parameters. Furthermore, non-Markovian dynamics significantly delay the discharge of the battery. Our study provides a pathway for constructing non-Markovian thermodynamic environments and harnessing non-Markovian effects to enhance the performance of quantum thermal devices.
In this work, we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy (a measure of the extractable work from a system under unitary evolution) monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.
We investigate ergotropy dynamics in a graphene-based quantum battery modeled as a four-level spin--valley system under different dissipative environments. The battery is charged via a Gaussian pulse and subsequently evolves under amplitude damping, dephasing, and both Markovian and non-Markovian reservoirs. We find that amplitude damping, while inducing energy loss, can stabilize non-passive steady states with finite ergotropy, whereas pure dephasing suppresses coherence and eliminates work extraction. On the other hand, non-Markovian memory slows ergotropy loss and enables partial recovery through information backflow. These results identify coherence and reservoir memory as essential resources for enhancing the long-time performance of graphene quantum batteries.