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arXiv:2306.06883 · Physical Review A

Cooling and work extraction under memory-assisted Markovian thermal processes

Yuancheng Liu, Xueyuan Hu

Published Sep 22, 2023• 1 citation
arXivHTMLPDF

Abstract

We investigate the limits on cooling and work extraction via Markovian thermal processes assisted by a finite-dimensional memory. Here the memory is a $d$-dimensional quantum system with trivial Hamiltonian and initially in a maximally mixed state. For cooling a qubit system, we consider two paradigms: cooling under coherent control and cooling under incoherent control. For both paradigms, we derive the optimal ground-state populations under the set of general thermal processes (TP) and the set of Markovian thermal processes (MTP), and we further propose memory-assisted protocols, which bridge the gap between the performances of TP and MTP. For the task of work extraction, we prove that when the target system is a qubit in the excited state the minimum extraction error achieved by TP can be approximated by Markovian thermal processes assisted by a large enough memory. Our results can bridge the performances of TP and MTP in thermodynamic tasks including cooling and work extraction.

DOI
10.1103/physreva.108.032216

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We investigate the limits on cooling and work extraction via Markovian thermal processes assisted by a finite-dimensional memory. Here the memory is a ddd-dimensional quantum system with trivial Hamiltonian and initially in a maximally mixed state. For cooling a qubit system, we consider two paradigms: cooling under coherent control and cooling under incoherent control. For both paradigms, we derive the optimal ground-state populations under the set of general thermal processes (TP) and the set of Markovian thermal processes (MTP), and we further propose memory-assisted protocols, which bridge the gap between the performances of TP and MTP. For the task of work extraction, we prove that when the target system is a qubit in the excited state the minimum extraction error achieved by TP can be approximated by Markovian thermal processes assisted by a large enough memory. Our results can bridge the performances of TP and MTP in thermodynamic tasks including cooling and work extraction.
We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model arbitrarily non-Markovian dynamics).Our approach is built on the notion of memory-assisted Markovian thermal processes, where memoryless thermodynamic processes are promoted to non-Markovianity by explicitly modeling ancillary memory systems initialized in thermal equilibrium states.Within this setting, we propose a family of protocols composed of sequences of elementary two-level thermalizations that approximate all transitions between energy-incoherent states accessible via thermal operations.We prove that, as the size of the memory increases, these approximations become arbitrarily good for all transitions in the infinite temperature limit, and for a subset of transitions in the finite temperature regime.Furthermore, we present solid numerical evidence for the convergence of our protocol to any transition at finite temperatures.We also explain how our framework can be used to quantify the role played by memory effects in thermodynamic protocols such as work extraction.Finally, our results show that elementary control over two energy levels at a given time is sufficient to generate all energy-incoherent transitions accessible via thermal operations if one allows for ancillary thermal systems.
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This paper compares the cooling performance of Markovian and non-Markovian quantum collisional models for nanoscale thermodynamic devices. A minimal setup is considered: a single qubit system repeatedly collides with qubit ancillas acting as a heat bath, while a local cooling “demon” operates on the system after each collision. Two regimes are analyzed: (i) a Markovian protocol where the system interacts with a fresh thermal ancilla at every step and the ancilla is subsequently rethermalized, and (ii) a non-Markovian protocol where the system repeatedly interacts with the same initially thermal environment qubit with no reset, allowing correlations (memory) to build up. A central contribution is an efficiency definition that explicitly includes all external energetic resources, counting both the energy removed by the demon and the otherwise hidden work cost of rethermalizing the ancillas in the Markovian implementation. The demon is modeled as an amplitude damping channel; via an explicit Stinespring dilation, the extracted energy is interpreted as heat dumped into an auxiliary cold reservoir, and the paper discusses how additional demon memory/erasure (Landauer) costs would further reduce operational efficiency. Numerical simulations show that the non-Markovian protocol can cool the system to much lower final energies and achieve substantially higher efficiency than the Markovian protocol across a wide range of collision (coupling) and damping strengths. The enhancement is traced to the finite environment’s initial energy and its capacity to store correlations as usable thermodynamic resources. The results emphasize that bounds and benchmarks derived under Markovian assumptions may significantly underestimate performance in finite, memoryful environments, and that reported efficiencies should be interpreted as upper bounds when demon implementation costs are not fully modeled.
Quantum thermodynamics studies how quantum systems and operations may be exploited as sources of work to perform useful thermodynamic tasks. In real-world conditions, the evolution of open quantum systems typically displays memory effects, resulting in a non-Markovian dynamics. The associated information backflow has been observed to provide advantage in certain thermodynamic tasks. However, a general operational connection between non-Markovianity and thermodynamics in the quantum regime has remained elusive. Here, we analyze the role of non-Markovianity in the central task of extracting work via thermal operations from general multitime quantum processes, as described by process tensors. By defining a hierarchy of four classes of extraction protocols, expressed as quantum combs, we reveal three different physical mechanisms (work investment, multitime correlations, and system-environment correlations) through which non-Markovianity increases the work distillable from the process. The advantages arising from these mechanisms are linked precisely to a quantifier of the non-Markovianity of the process. These results show in very general terms how non-Markovianity of any given quantum process is a fundamental resource that unlocks an enhanced performance in thermodynamics.
We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.
Abstract We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.