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QFE-1: A Falsifiable Null-Test Framework for Single-Reservoir Quantum Work Extraction

Luke Ivan Dobner

Published Sep 21, 2026• 0 citations
Publisher

Abstract

QFE-1 is a falsifiable quantum-thermodynamics research proposal for testing whether an explicit quantum battery can gain useful non-equilibrium free energy from a single equilibrium thermal reservoir while every declared auxiliary resource, including control, memory, coherence, timing and correlations — is returned to its reference condition and externally supplied work is independently metered. Version 2.0 adds a formal weak-coupling free-energy bound, a quantitative superconducting-circuit reference regime, a thermal master-equation baseline, an analytical null calculation showing energy gain without work gain, explicit false-positive controls, strong-coupling safeguards, a staged experimental programme, and pre-registered falsification criteria. No experimental violation of thermodynamics or discovery of perpetual motion is claimed.

DOI
10.5281/zenodo.22879529

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QFE-1 is a falsifiable quantum-thermodynamics research proposal for testing whether an explicit quantum battery can gain useful non-equilibrium free energy from a single equilibrium thermal reservoir while every declared auxiliary resource, including control, memory, coherence, timing and correlations — is returned to its reference condition and externally supplied work is independently metered. Version 2.0 adds a formal weak-coupling free-energy bound, a quantitative superconducting-circuit reference regime, a thermal master-equation baseline, an analytical null calculation showing energy gain without work gain, explicit false-positive controls, strong-coupling safeguards, a staged experimental programme, and pre-registered falsification criteria. No experimental violation of thermodynamics or discovery of perpetual motion is claimed.
QFE-1N is the numerical companion to QFE-1, providing reproducible null tests for a superconducting-circuit implementation of the proposed quantum-fluctuation engine framework. The study models a transmon-like two-level system coupled to a truncated resonator battery and an equilibrium thermal reservoir using a detailed-balance Lindblad master equation. The simulations show thermal energy transfer into the resonator without the appearance of anomalous ergotropy or non-equilibrium free energy, consistent with standard quantum thermodynamics. The package includes the numerical model, simulation code, data, figures, reproducibility environment and verification files. No violation of the second law or experimental evidence of single-reservoir work extraction is claimed.
The resource-theoretic approach to quantum thermodynamics typically assumes perfect knowledge of the thermal equilibrium state, an idealization incompatible with finite experimental precision. We develop a framework for equilibrium uncertainty by representing the equilibrium reference as a set of candidate states. Under a generic geometric condition, we prove a no-go theorem that sharply limits athermality ``purification'': converting an uncertain athermal state into a definite target is either trivial or impossible. We then derive exact one-shot entropic characterizations of work extraction and formation for two work-storage models, a clean battery with known equilibrium and a dirty battery with uncertain equilibrium. Both models exhibit strong asymptotic irreversibility even under arbitrarily small uncertainty. An explicit example reveals two distinct extremes: clean batteries display a bound-entanglement-like phenomenon, with positive formation cost but zero extractable work, whereas dirty batteries allow positive work extraction but require infinite formation cost. These phenomena show that equilibrium uncertainty is not a minor perturbation of the standard theory, but a structural ingredient that fundamentally reshapes the limits of quantum thermodynamics.
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 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.
Thermally charged quantum batteries provide a stable and easy-to-have energy resource, but remain passive and therefore do not allow useful energy extraction on demand via unitary operations. We introduce a time-dependent stirring protocol that activates a thermally charged quantum battery through a time-dependent coupling to an auxiliary activator, thereby generating correlations that drive the battery into an active state. Accounting explicitly for the energetic cost of the stirring process, the entropic cost of correlation generation and the activation time, we derive bounds on the maximal net extractable energy. Incorporating projective measurement on the activator and exploiting the information gained through the measurement further enhances the extractable energy. As an experimentally relevant example, we analyze a waveguide-QED setup where a harmonic-oscillator battery (waveguide) is stirred and monitored by a two-level system. We characterize the performance of the protocol in terms of net extractable energy (net ergotropy) and power output.
We investigate the charging dynamics and thermodynamic performance of a wireless quantum battery system mediated by a common structured bosonic environment. By employing a unified resource-theoretic analysis, we elucidate the distinct roles of non-Markovian memory effects and coupling symmetry in regulating energy transfer. In the Markovian weak-coupling regime, we identify a transformative mechanism where the dynamic reconstruction of l1l_1l1​-norm coherence compensates for the monotonic decay of first-order coherence to sustain energy transport. Conversely, the non-Markovian strong-coupling regime facilitates a cooperative resonance, characterized by the synchronized oscillation of entanglement and stored energy induced by environmental backflow. Furthermore, we reveal that coupling symmetry acts as a critical control parameter: while asymmetric coupling favoring the battery optimizes energy gain in memoryless environments, symmetric coupling under strong interactions unlocks a dark-state protection mechanism, effectively trapping energy within a decoherence-free subspace. Finally, a thermodynamic analysis based on ergotropy demonstrates that first-order coherence establishes the activation threshold for incoherent work, whereas l1l_1l1​-norm coherence serves as the explicit fuel for coherent work extraction. These findings provide a refined theoretical framework for engineering environment-assisted quantum energy storage devices.