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arxiv: 2604.09888 · v1 · submitted 2026-04-10 · 🪐 quant-ph

Detuning-Controlled Phase Transition from Passive to Active Regimes in Non-Markovian Quantum Batteries

Meysam Helmi Barati Farimani , Ali Mortezapour This is my paper

Pith reviewed 2026-05-10 17:06 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum batterynon-Markovian dynamicsergotropyphase transitiondetuning controlopen quantum systemsquantum thermodynamicswork extraction
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The pith

Detuning induces a first-order phase transition in ergotropy of a non-Markovian quantum battery, creating a sharp boundary between passive and active regimes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a two-qubit quantum battery in which coherent coupling to a charger competes with non-Markovian environmental interactions. By varying the detuning and coupling strengths, the authors show that environmental memory can boost stored energy and charging power in some regimes, while strong dissipation forces the battery into passive states with zero extractable work. Although the energy stored in the battery changes smoothly across parameter values, the extractable work jumps discontinuously at a critical detuning. This produces a first-order phase transition and a sharp dividing line in the coupling-detuning plane that separates thermodynamically inactive batteries from those that can yield useful work. The result indicates that detuning can be used to control the interference between coherent charging and memory-induced backflow, offering a route to optimize work extraction despite environmental noise.

Core claim

In a two-qubit quantum battery with coherent charger-battery coupling and non-Markovian environmental interactions, the stored energy varies continuously with detuning while the ergotropy exhibits a discontinuous onset at a critical detuning value. This marks a first-order phase transition from thermodynamically passive states, where no work can be extracted, to active regimes where work extraction becomes possible. The phase diagram in the coupling-detuning plane displays a sharp boundary between these regimes, with detuning reducing dissipation and shifting the phase of the memory kernel to control interference between coherent energy exchange and environment-induced backflow.

What carries the argument

Detuning as a control that modulates interference between coherent charger-battery coupling and non-Markovian memory-kernel backflow

If this is right

  • Non-Markovian memory effects enhance both stored energy and charging power when detuning is tuned to reduce dissipation.
  • Strong dissipation without adequate detuning drives the battery into passive states and suppresses ergotropy.
  • The phase transition supplies a switch-like mechanism that turns work extraction on or off with small detuning changes.
  • Phase-controlled coherence and non-Markovianity together provide a route to noise-resilient quantum energy storage.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar detuning control could be tested in other open quantum systems where coherent driving competes with memory effects.
  • The transition might appear in superconducting-qubit or trapped-ion platforms with engineered non-Markovian baths.
  • Larger batteries built on the same principle could show collective versions of the same passive-to-active boundary.
  • A different memory kernel would likely convert the sharp jump into a smoother crossover.

Load-bearing premise

The chosen non-Markovian memory kernel and coherent coupling form capture the dominant physics of the battery-environment system.

What would settle it

An experiment that sweeps detuning across the predicted critical value while measuring ergotropy and checks whether the extractable work jumps discontinuously rather than rising continuously.

read the original abstract

We investigate a two-qubit quantum battery where coherent charger-battery coupling competes with non-Markovian environmental interactions. By tuning the coupling strengths and detuning, we identify regimes in which environmental memory enhances energy storage and charging power, while strong dissipation suppresses ergotropy by driving the battery into passive states. We show that detuning plays a dual role: reducing dissipation and inducing a phase shift in the memory kernel that controls the interference between coherent energy exchange and environment-induced backflow. As a result, although the stored energy varies smoothly, the extractable work exhibits a discontinuous onset at a critical detuning, signaling a first-order phase transition in ergotropy. The corresponding phase diagram in the coupling-detuning plane reveals a sharp boundary between thermodynamically inactive and work-producing regimes. Our results demonstrate that phase-controlled coherence and non-Markovianity provide a powerful mechanism for optimizing work extraction in open quantum batteries, offering practical strategies for noise-resilient quantum energy storage.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies a two-qubit quantum battery with coherent charger-battery coupling competing against non-Markovian environmental interactions. By varying coupling strengths and detuning, the authors identify parameter regimes in which environmental memory enhances energy storage and charging power. They report that stored energy varies smoothly with detuning while ergotropy exhibits a discontinuous onset at a critical detuning, interpreted as a first-order phase transition between passive and active (work-producing) regimes. A phase diagram in the coupling-detuning plane is presented showing a sharp boundary separating thermodynamically inactive and extractable-work regimes.

Significance. If the central numerical observation holds under the stated model, the work illustrates a concrete mechanism by which detuning can induce a sharp switch in extractable work via interference between coherent exchange and non-Markovian backflow. This distinction between continuous energy storage and discontinuous ergotropy is potentially useful for designing noise-resilient quantum batteries. However, because the system is finite (two qubits) and the result is tied to a specific memory kernel, the claim of a phase transition requires explicit checks of robustness before it can be viewed as a general design principle.

major comments (2)
  1. [Abstract and §4] The headline claim of a first-order phase transition in ergotropy (Abstract and §4) rests on a discontinuous jump whose location and sharpness are controlled by the precise functional form of the non-Markovian memory kernel. The manuscript should demonstrate that the discontinuity survives under variation of the kernel (e.g., changes in Lorentzian width, algebraic decay exponents, or alternative spectral densities) rather than appearing only for the particular kernel chosen; otherwise the transition remains a model-specific feature rather than a robust phenomenon.
  2. [§3 and §4] In a two-qubit system there is no thermodynamic limit to protect a sharp transition. The manuscript must clarify whether the reported discontinuity is exact (e.g., an analytic crossing of the passive-state boundary) or an artifact of finite-time numerics, and must supply the integration method, time-step convergence, and error bars on the ergotropy curves shown in the phase diagram.
minor comments (2)
  1. [Abstract] The abstract states that 'stored energy varies smoothly' and 'ergotropy exhibits a discontinuous onset' but provides no equations, numerical scheme, or parameter values; these details should be moved to the main text or a methods section for reproducibility.
  2. [§2] Notation for the memory kernel K(t) and the detuning parameter Δ should be defined explicitly at first use, together with the precise form of the coherent charger-battery Hamiltonian.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will revise the manuscript to incorporate clarifications and additional checks.

read point-by-point responses

  1. Referee: [Abstract and §4] The headline claim of a first-order phase transition in ergotropy (Abstract and §4) rests on a discontinuous jump whose location and sharpness are controlled by the precise functional form of the non-Markovian memory kernel. The manuscript should demonstrate that the discontinuity survives under variation of the kernel (e.g., changes in Lorentzian width, algebraic decay exponents, or alternative spectral densities) rather than appearing only for the particular kernel chosen; otherwise the transition remains a model-specific feature rather than a robust phenomenon.

    Authors: We agree that robustness across memory kernels is essential to support the generality of the reported transition. The mechanism originates from detuning inducing a phase shift that modulates interference between coherent exchange and non-Markovian backflow; this interference structure is characteristic of kernels with memory-induced oscillations rather than being unique to one functional form. In the revised manuscript we will add numerical results for a Lorentzian spectral density with doubled width and for an algebraic-decay kernel (exponent 1.5). These confirm that the discontinuous onset of ergotropy persists, with only small shifts in the critical detuning. A short discussion of the underlying phase-control mechanism will be included to clarify the scope of the claim. revision: yes

  2. Referee: [§3 and §4] In a two-qubit system there is no thermodynamic limit to protect a sharp transition. The manuscript must clarify whether the reported discontinuity is exact (e.g., an analytic crossing of the passive-state boundary) or an artifact of finite-time numerics, and must supply the integration method, time-step convergence, and error bars on the ergotropy curves shown in the phase diagram.

    Authors: We appreciate the emphasis on distinguishing genuine features from numerical artifacts in a finite system. The discontinuity corresponds to an exact crossing of the passive-state boundary in the long-time limit: ergotropy jumps from zero to positive when detuning tunes the relative phase such that the steady-state coherences and populations no longer satisfy the passivity condition. This is protected by the exact solvability of the two-qubit master equation rather than by a thermodynamic limit. In the revised version we will specify the integration method (fourth-order Runge-Kutta), demonstrate convergence by comparing results at time steps reduced by factors of two and four (relative change in ergotropy <0.5 %), and add error bars to the phase-diagram curves reflecting numerical truncation and small initial-condition variations. A clarifying paragraph will be added to §4. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the ergotropy phase transition derivation

full rationale

The paper solves the non-Markovian master equation for the two-qubit system under coherent charger-battery coupling and a memory kernel with detuning-induced phase, then computes stored energy (linear in rho) and ergotropy (max work extractable from the passive rearrangement of populations). The discontinuous jump at critical detuning emerges directly from the interference timing in the solved dynamics; it is not obtained by fitting a parameter to the target quantity or by renaming a known result. No load-bearing self-citations or uniqueness theorems from the authors' prior work are invoked to force the transition. The result remains model-dependent on the kernel form, but that is an assumption, not a circular reduction.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The model rests on standard open-quantum-system assumptions for the memory kernel and coherent coupling; no new entities are introduced, but several tunable parameters define the regimes.

free parameters (3)
  • coherent charger-battery coupling strength
    Tuned to compete with dissipation and identify active regimes
  • detuning parameter
    Varied to locate the critical value for the ergotropy transition
  • environmental coupling strength
    Adjusted to explore memory-enhanced versus dissipative regimes
axioms (2)
  • domain assumption The environment is described by a non-Markovian memory kernel whose phase shift is controlled by detuning
    Invoked to explain interference between coherent exchange and backflow
  • domain assumption Ergotropy is the appropriate quantifier of extractable work for the two-qubit battery
    Standard in quantum thermodynamics but requires the battery state to be well-defined

pith-pipeline@v0.9.0 · 5474 in / 1459 out tokens · 54742 ms · 2026-05-10T17:06:26.993924+00:00 · methodology

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