The quantum battery capacity is introduced in this Letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and entanglement.
The quantum battery capacity is introduced in this Letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and entanglement.
Quantum batteries, consisting of quantum cells, are anticipated to surpass their classical counterparts in performance because of the presence of quantum correlations. A recent theoretical study has introduced quantum battery capacity, which is defined according to the highest and the lowest energy during the charging and discharging procedures. Here, we present an experimental verification of quantum battery capacity and its relationships with other quantum characteristics of batteries using two-photon states. This reveals a distinguished feature of quantum battery capacity and its trade-off relationship with the entropy of the battery state, as well as with measures of coherence and entanglement.
Abstract The rapid advancements in quantum information science and quantum thermodynamics have led to increasingly interdisciplinary innovations. One notable development is the concept of the ergotropic gap, defined as the difference between global and local ergotropy. Building on this foundation, multipartite ergotropic gap indicators have been proposed to enhance methods of entanglement classification [Phys. Rev. A 109 , 062427 (2024)]. Motivated by this perspective, the thermodynamic notion of quantum battery capacity—closely related to ergotropy and defined as the energy difference between maximally and minimally achievable states under unitary evolution—is examined to address state ordering problems. The investigation focuses on comparing state orderings using three measures: battery capacity, entanglement of formation, and quantum discord, with particular emphasis on two‐qubit Bell‐diagonal states. Remarkably, certain classes of these states exhibit identical ordering patterns across all three measures under specific conditions.
Abstract The distribution relationship of quantum battery capacity is investigated. First, it is proved that for two‐qubit ‐states, the sum of the subsystem battery capacities does not exceed the total system's battery capacity, and the conditions are provided under which they are equal. Then define the difference between the total system's and subsystems' battery capacities as the residual battery capacity () and show that this can be divided into coherent and incoherent components. Furthermore, it is observed that this capacity monogamy relation for quantum batteries extends to general ‐qubit states and any ‐qubit state's battery capacity distribution can be optimized to achieve capacity gain through an appropriate global unitary evolution. Specifically, for general three‐qubit states, stronger distributive relations are derived for battery capacity. Quantum batteries are believed to hold significant potential for outperforming classical counterparts in the future. These findings contribute to the development and enhancement of quantum battery theory.
Ergotropy--a key figure of merit for quantum battery (QB) performance--plays a crucial role. However, the dynamics and physical mechanisms governing ergotropy evolution remain open challenges. Here, we investigate the ergotropy of a general QB model and find that the charging process is accompanied by the variation and inversion of the energy level populations. In the absence of population inversion, the ergotropy is fully consistent with coherent ergotropy; in local and global population inversion, it is determined by both coherent and incoherent ergotropy. Via random sampling of quantum states and Hamiltonians, we show that coherence and the participation ratio enhance coherent ergotropy, whereas incoherent ergotropy--whether enhanced, unchanged, or suppressed--depends on diagonal entropy, the participation ratio, and energy level population ordering. We demonstrate that the ergotropy lower bound is incoherent ergotropy, the upper bound is the QB stored energy, and enhanced QB purity suppresses locked energy and boosts charging efficiency. Furthermore, we use the Tavis-Cummings (TC) and Jaynes-Cummings (JC) batteries as paradigms to validate our findings. Our work elucidates ergotropy underlying mechanisms in general QBs and establishes a rigorous framework for optimizing ergotropy and charging efficiency, paving the way for high-performance quantum energy-storage devices.
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.
We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two-level systems.