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Exergy and quantum batteries

F. H. Kamin, S. Salimi

Published Mar 26, 2024• 0 citations
Publisher

Abstract

The study of quantum thermodynamics has led to the development of quantum batteries. These devices use quantum advantages to store and extract useful energy from physical systems. Ergotropy is the maximum work that can be extracted from a quantum system by cyclic unitary operations. When external thermal baths couple with the quantum battery, there is energy loss due to thermal effects on the system. In some cases, a part of the total energy available in the system cannot be stored as ergotropy. Therefore, it is important to consider the amount of residual energy that cannot be extracted as useful work from quantum batteries by unitary processes. To better understand the amount of energy lost during work extraction, it is necessary to examine the constraint of unitary processes. The system exergy represents the maximum amount of work that can be extracted from the system while bringing it into equilibrium with a thermal bath. It can be separated into two parts: ergotropy and residual energy. Thus, the present chapter describes the relationship between exergy and its potential benefits and effects on the performance of quantum batteries.

DOI
10.5772/intechopen.1004642

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The study of quantum thermodynamics has led to the development of quantum batteries. These devices use quantum advantages to store and extract useful energy from physical systems. Ergotropy is the maximum work that can be extracted from a quantum system by cyclic unitary operations. When external thermal baths couple with the quantum battery, there is energy loss due to thermal effects on the system. In some cases, a part of the total energy available in the system cannot be stored as ergotropy. Therefore, it is important to consider the amount of residual energy that cannot be extracted as useful work from quantum batteries by unitary processes. To better understand the amount of energy lost during work extraction, it is necessary to examine the constraint of unitary processes. The system exergy represents the maximum amount of work that can be extracted from the system while bringing it into equilibrium with a thermal bath. It can be separated into two parts: ergotropy and residual energy. Thus, the present chapter describes the relationship between exergy and its potential benefits and effects on the performance of quantum batteries.
Work extraction protocol is always a significant issue in the context of quantum batteries, in which the notion of ergotropy is used to quantify a particular amount of energy that can be extracted through unitary processes. Given the total amount of energy stored in a quantum system, quantifying wasted energy after the ergotropy extraction is a question to be considered when undesired coupling with thermal reservoirs is taken into account. In this paper, we show that some amount of energy can be lost when we extract ergotropy from a quantum system and quantified by the exergy of passive states. Through a particular example, one shows that ergotropy extraction can be done by preserving the quantum correlations of a quantum system. Our study opens the perspective for new advances in open system quantum batteries able to explore exergy stored as quantum correlations.
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In this study, we investigate the effectiveness of entropic uncertainty relations (EURs) in discerning the energy variation in quantum batteries (QBs) modelled by battery-charger field in the presence of bosonic and fermionic reservoirs. Our results suggest that the extractable works (exergy and ergotropy) have versatile characteristics in different scenarios, resulting in a complex relationship between tightness and extractable work. It is worth noting that the tightness of the lower bound of entropic uncertainty can be a good indicator for energy conversion efficiency in charging QBs. Furthermore, we disclose how the EUR including uncertainty and lower bound contributes to energy conversion efficiency in the QB system. It is believed that these findings will be beneficial for better understanding the role of quantum uncertainty in evaluating quantum battery performance.
We show that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process. Systems in the equilibrium states of these processes serve as batteries, storing energy. The dissipative process that brings the battery to the active equilibrium state is driven by an agent that couples the battery to thermal systems. The second law of thermodynamics imposes a work cost for the process; however, no work is needed to keep the battery in that charged state. We consider simple examples of these batteries and discuss situations in which the charged state has full population inversion, in which case the extractable work is maximal, and circumstances in which the efficiency of the process is maximal.
Ergotropy provides a fundamental measure of the extractable work from a quantum system and, consequently, of the maximal useful energy, or charge, stored within it. Understanding how this quantity can be manipulated and transformed efficiently is crucial for advancing quantum energy management technologies. Here, we introduce and formalize the concepts of isoergotropic states and ergotropy-preserving operations, which reorganize the internal structure of ergotropy while keeping its total value unchanged. These ideas are illustrated for both discrete (two-level systems) and continuous-variable systems (single-mode Gaussian states). In each case, we show how ergotropy-preserving operations redistribute the respective coherent-incoherent and displacement-squeezing components. We further examine the thermodynamic exchanges accompanying ergotropy-preserving operations, including variations in energy and entropy, and demonstrate that these transformations can be dynamically implemented through standard beam-splitter-type interactions with an auxiliary system. Finally, we discuss the practical implications of isoergotropic states and operations in optimizing charging protocols and mitigating charge loss in open quantum batteries.
We construct a central-spin battery model affected by noise or thermal bath and consider the impact of environment on battery performance. In a noisy environment, we show that the steady-state energy and ergotropy are related to the number of spins exposed to the noisy channel. In addition, we reveal the relationship between the steady-state energy and ergotropy with the quantum information lost in the battery. In a thermal bath, we find that the higher the mean occupation number of the thermal bath, the greater the steady-state energy. In particular, we find that, in two different environments, the steady-state energy and ergotropy are related to the effective magnetic-field strength of battery BBB, but not charger hhh. It is worth noting that, in the central-spin model, when BBB is a constant and $|h/B\ensuremath{-}1|$ reaches a certain value, the steady-state energy and ergotropy with noise or thermal bath are always greater than or equal to the maximum energy and ergotropy of the corresponding closed battery. At the same time, we generalize the conclusions to the two-qubit, two-harmonic-oscillator, and harmonic-oscillator-qubit models.