This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.
This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.
Work extraction is a fundamental aspect in thermodynamics. In the context of quantum physics, ergotropy quantifies the maximum amount of work that can be obtained from quantum system through cyclic unitary process. In this work, the steady-state ergotropy of two coupled qubit, each interacting locally with its individual boson or fermion reservoir, will be examined. In this work, both equilibrium and non-equilibrium scenarios for bosonic and fermionic environments interacting with the qubits will be considered. In scenarios where two coupled qubits embedded within equilibrium boson reservoirs, it has been observed that the temperature of the reservoirs and the inter-qubits interaction strangth act as detrimental factors in work extraction. In the case of fermionic equilibrium reservoirs, it will be observed that ergotropy grows monotonically with the reservoirs chemical potential. In the non-equilibrium boson reservoirs, the temperature difference between the two reservoirs is a destructive factor for ergotropy. In non-equilibrium fermion reservoirs, the situation is somewhat more complicated. For r base chemical potential values that are smaller than the qubit transition frequency, the behavior of ergotropy is non-monotonic. However, for base chemical potential values that are larger than the transition frequency, ergotropy grows monotonically with the reservoirs chemical potential difference. Also, we study the situation in which the coupled qubits are asymmetric. It is observed that the maximum work will be extracted in the situation where the coupled qubits within both boson and fermion reservoirs be symmetric .
This study examines the steady state characteristics of work extraction in a two cell and three cell quantum battery interacting with multiple thermal reservoirs. Employing the quantum master equation framework within the Born-Markov approximation, we explore the non equilibrium dynamics governing energy storage and extraction in the system. Our analysis focuses on the influence of thermal gradients across the reservoirs and the impact of inter cell coupling strength on the battery performance. The findings demonstrate that an increase in the middle reservoir temperature substantially enhances the extractable work, underscoring the pivotal role of thermal bath amplification in optimizing energy storage efficiency. Furthermore, we uncover a non trivial relationship between ergotropy and the coupling strength among the quantum cells, revealing the existence of an optimal coupling regime that maximizes energy extraction. Beyond this threshold, excessive coupling induces energy localization, thereby diminishing the system efficiency. These insights provide a theoretical foundation for the strategic design of high performance quantum batteries by harnessing thermal gradients and interaction driven control mechanisms.
Understanding the generation and activation of ergotropy, the maximum work extractable by cyclic unitary operations, is central to quantum battery research. Positive-temperature thermal states are passive, whereas nonequilibrium environments can sustain nonpassive steady states with nonzero ergotropy. However, the full secular approximation commonly used in Lindblad descriptions can suppress steady-state coherence and obscure its contribution to ergotropy. Using a Bloch-Redfield master equation beyond the full secular approximation, we investigate the ergotropy of the nonequilibrium steady state (NESS) of two exchange-coupled qubits connected to independent thermal reservoirs. The NESS ergotropy of two qubits with the same frequency is entirely coherent and grows quadratically with temperature bias near equilibrium. In contrast, detuned qubits can exhibit incoherent ergotropy. We derive an exact analytical criterion for its activation and show that activation requires the hotter reservoir to be coupled to the qubit with the higher bare frequency. Comparing NESSs obtained with and without full secularization reveals quantitative and qualitative differences in ergotropy that reflect changes in both its coherent and incoherent contributions. The results clarify the mechanisms of NESS ergotropy activation and demonstrate the importance of retaining steady-state coherence beyond the full secular approximation when characterizing stationary work resources.
Quantum batteries, as highly efficient energy storage devices, have garnered significant research interest. A key challenge in their development is to maximize the extractable energy (ergotropy) when operating within a finite-temperature reservoir. To address this, we applied quantum feedback control to the charger and investigated the effects of fermionic and bosonic thermal reservoirs on the performance of quantum batteries, including stored energy, ergotropy, and charging efficiency, in an open environment. Our findings reveal that, regardless of the type of thermal reservoir, the system exhibits optimal charging parameters. In particular, in a fermionic thermal reservoir, increasing the environmental temperature enhances battery performance, enabling stable and efficient charging. In contrast, within a bosonic thermal reservoir, higher temperatures hinder energy storage and extraction, significantly reducing charging efficiency. Additionally, we explored the impact of battery size and found that, under a fermionic reservoir, increasing the battery size appropriately can further improve performance.
We investigate work extraction in open quantum batteries composed of interacting spin chains weakly coupled to engineered environments. Focusing on two- and four-qubit XX models initially prepared in thermal Gibbs states, we analyze how dissipation and dephasing, acting either locally or collectively, can generate and shape ergotropy during both transient and steady-state dynamics. By introducing a continuous interpolation between parallel and collective noise channels, we systematically characterize the impact of environmental structure on work extractability. We show that purely dissipative dynamics can activate finite ergotropy from completely passive thermal states, giving rise to temperature-dependent transient regimes where hotter initial states temporarily outperform colder ones in an ergotropic Mpemba-like fashion. In contrast, collective dissipation leads to steady states whose passivity crucially depends on the initial temperature and system size, a behavior we trace back to the emergence of non-trivial dark subspaces. Finally, we demonstrate that dephasing channels suppress both transient advantages and steady-state work extraction, highlighting the qualitative difference between dissipative and dephasing environments.
We investigate how the spatial arrangement of environment channel influences the dynamics of coherence and work extraction in a two-qubit quantum battery with resonant qubits coupled through an XY-exchange interaction. Qubit B is attached to a finite-temperature thermal bath, while RTN noise is applied either to qubit A or to qubit B, depending on whether it is in a separated or co-located configuration, respectively. Two complementary product states are considered to initialise the coherence on different qubits. The dynamics are evaluated using local l1-norm coherence, global ergotropy and the global-local ergotropy gap. The results suggest that a stronger exchange interaction enhances the redistribution of coherence without necessarily improving retention of extractable work. For the parameter investigated, the greater global ergotropy is retained in the case of the co-located configuration, especially when the initially coherent qubit is not directly affected by the RTN. However, the configuration provides the largest global-local ergotropy gap, which varies with the exchange interaction, initial state and thermal coupling. Suppression of the gap at large J is typically observed in the case of stronger thermalisation, although enhancement of intermediate-coupling may occur. These results establish that total extractable work, local coherence and collective work advantage quantify the distinct aspects of quantum battery performances. The initial distribution of coherence and the spatial arrangement thus provide complementary mechanisms for regulating locally and collectively extractable work in interacting open quantum batteries.