Probing quasiperiodic spectral accessibility with a finite-rate quantum Otto cycle

The gist: A finite-rate quantum Otto cycle can use quasiperiodic spectral accessibility as a thermodynamic probe to reveal which parts of the spectrum become dynamically accessible and thermodynamically relevant during a driven transformation.

How it works

1. The study uses a generalized AubryAndr´e-Harper chain as the working medium, where the Hamiltonian is varied between different quasiperiodic regimes (Page 3).

2. A finite-time Otto cycle contains two distinct clocks: one for isolated work strokes where the Hamiltonian changes and another for thermal contacts where populations redistribute (Page 4).

3. The driving rate is treated as a physical control parameter, defining a finitetime operating diagram that connects microscopic population transfer to mean thermodynamic output and the complete work distribution (Page 4).

4. Spectral accessibility is operationally described by the portion of the evolving spectrum that contributes appreciably to this finite-rate thermodynamic response, determined jointly by dynamical coupling, thermal occupation, and energetic consequences (Page 4).

Key Findings on Spectral Accessibility

The static quasiperiodic regime does not impose a universal ordering on finite-rate work fluctuations.

The results show that extended, near-critical, and crossing protocols exchange their fluctuation ordering between the slow-driving, finite-rate, and state-frozen regimes (Page 6). The relevant distinction is therefore dynamical, with the statistics depending on which parts of the spectrum become accessible during the stroke rather than on the static phase label alone (Page 6).

"Positive mean work can reappear while the population transfer dynamics remain strongly nonadiabatic because finite-rate population transfer is redistributed toward energetically less costly channels rather than suppressed."

This behavior occurs because positive-work cycles form a majority over a finite window of driving rates, even though the mean work remains negative (Page 6). The full work distribution reveals a further separation where the narrowest isolated avoided crossing contributes only a small fraction of this response, suggesting that the operating boundary reflects the collective action of many thermally active transitions rather than a single minimum-gap bottleneck (Page 6).

Work Fluctuations and Distinct Criteria

Positive mean work and typical-cycle output recover at distinct rates.

The contours in the two heat maps are separated, showing that a majority of cycles can already produce positive work while the mean is still negative (Page 8). The fluctuation scale depends on the driving protocol as well as the static spectral regime (Page 4).

The negative-work sector is concentrated in the thermally occupied low-energy manifold.

The conditional energetic loss increases strongly with branch displacement and is concentrated in the thermally occupied low-energy manifold, where at a representative point, the lowest 32 hot-side branches contain 50.8% of the Gibbs population but generate 71.1% of the negative cycles (Page 8).

Role of Finite Thermal Contacts and Repeated Cycles

Finite thermal contacts introduce a second boundary in addition to the work-stroke boundary of Sec. III.

Incomplete renewal leaves population memory in the stationary cycle, making thermalization itself a second accessibility constraint while also adding the contact duration to the performance problem (Page 12). The required symmetric reset strength depends strongly on the chosen finiterate protocol (Page 12).

The same incomplete renewal generates intercycle correlations.

These correlations remain weak near the use of finite contacts, but they become quantitatively important near the contact threshold, where long-time counting statistics are needed to characterize the fluctuations consistently (Page 15). The one-cycle variance already approximates the longtime variance closely at the maximum-power strong-contact point (Page 14).

Conclusion

The finite-rate Otto cycle resolves a hierarchy of dynamical information that is hidden in the usual slow driving and state-frozen limits, establishing that thermodynamic recovery does not coincide with microscopic energy-ordered following (Page 15). Spectral accessibility is determined jointly by dynamical coupling, thermal occupation, and energetic weight rather than by a single spectral scale (Page 15). This provides an operational route for resolving finite-rate spectral structure through quantum thermodynamic observables (Page 15).

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Probing quasiperiodic spectral accessibility with a finite-rate quantum Otto cycle Shujie Cheng, Lucas C. C´eleri, Norton G. de Almeida, Gao Xianlong, and G. D. de Moraes Neto are the authors of this paper (Page 1).

1. Quasiperiodic systems combine sharply different spectral and localisation regimes with a dense hierarchy of dynamical time scales (Page 1).

2. A finite-rate quantum Otto cycle can use this structure as a thermodynamic probe, revealing which parts of the spectrum become dynamically accessible and thermodynamically relevant during a driven transformation (Page 1).

3. For a generalized AubryAndr´e-Harper chain, the resulting response is not determined by the static quasiperiodic regime alone: extended, near-critical, and crossing protocols do not exhibit universal ordering of work fluctuations (Page 1).

The same spectral accessibility separates thermodynamic recovery from microscopic adiabatic recovery.

The same spectral accessibility separates thermodynamic recovery from microscopic adiabatic recovery (Page 1). Positive mean work can reappear while the population transfer dynamics remain strongly nonadiabatic because finite-rate population transfer is redistributed toward energetically less costly channels rather than suppressed (Page 1).

The full work distribution reveals a further separation, with a finite rate window in which positive-work cycles form a majority although the mean work remains negative.

The full work distribution reveals a further separation, with a finite rate window in which positive-work cycles form a majority although the mean work remains negative (Page 1).

Finite thermal contacts preserve this picture while introducing a second time scale and intercycle memory.

Finite thermal contacts preserve this picture while introducing a second time scale and intercycle memory (Page 1). Quantum Otto cycles can therefore provide a fluctuation-resolved thermodynamic probe of quasiperiodic spectral accessibility, complementary to direct spectroscopic and eigenstate-resolved diagnostics (Page 1).

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Quasiperiodic lattices occupy an intermediate position between periodic order and random disorder. They are deterministic and aperiodic, yet can support localisation, critical states, mobility edges, and fractal spectral structure without quenched randomness (Page 2).

1. The diagonal-plus-off-diagonal AubryAndr´e-Harper Hamiltonian is used to model the working medium (Page 3).

2. The finite-time Otto cycle compares three paths within this same Hamiltonian family: one remains on the extended side, another approaches the static boundary, and the third crosses it (Page 4).

The relevant distinction is therefore dynamical, with the statistics depending on which parts of the spectrum become accessible during the stroke, rather than on the static phase label alone.

The relevant distinction is therefore dynamical, with the statistics depending on which parts of the spectrum become accessible during the stroke, rather than on the static phase label alone (Page 6).

"Along the crossing path, this produces two further separations. Positive mean work recovers, while the population-transfer map remains strongly nonadiabatic, with a transition-resolved decomposition showing that the transferred population shifts toward energetically less costly channels."

Along the crossing path, this produces two further separations. Positive mean work recovers while the population-transfer map remains strongly nonadiabatic, with a transition-resolved decomposition showing that the transferred population shifts toward energetically less costly channels (Page 6).

Finite thermal contacts extend this picture beyond the complete-reset cycle.

Finite thermal contacts extend this picture beyond the complete-reset cycle (Page 1). Incomplete renewal introduces a second dynamical time scale, modifies work, power, efficiency, and fluctuations, and generates correlations between successive cycles (Page 1).

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A finite-time Otto cycle contains two physically distinct clocks. During the isolated work strokes the Hamiltonian changes, and the relevant time is the duration available for the state to reorganise through the evolving spectrum. During thermal contacts, the Hamiltonian is fixed while the reservoirs redistribute populations, and the relevant time is the duration available for relaxation (Page 4).

1. The Gibbs populations are determined by corner states A (hot Gibbs state of H(rh)) and C (cold Gibbs state of H(rc)), while B and D are generated by unitary work strokes (Page 4).

2. Work is calculated as Wout = Qh + Qc, where Qh = UA − UD and Qc = UC − UB (Page 4).

If only the endpoints were specified, this classification would say nothing about the speed with which the spec

If only the endpoints were specified, this classification would say nothing about the speed with which the spec (Page 4).

**"Finite-time engines can exhibit broad and asymmetric work distributions [28, 29], threshold probabilities distinguish likely from average work extraction [30], and mean-to-fluctuation ratios provide separate measures of output precision [31–34]." **

Finite-time engines can exhibit broad and asymmetric work distributions [28, 29], threshold probabilities distinguish likely from average work extraction [30], and mean-to-fluctuation ratios provide separate measures of output precision [31–34] (Page 4).

1. Direct spectral accessibility probing for quasiperiodic systems: The improved AI can use a finite-rate quantum Otto cycle to reveal which parts of the spectrum become dynamically accessible and thermodynamically relevant during a driven transformation, moving beyond static phase labels alone.

2. Predictive modeling of work fluctuations: The system can predict positive mean work even when the mean work remains negative, by identifying a finite rate window in which positive-work cycles form a majority although the mean work remains negative.

3. Characterization of transition pathways: The AI can distinguish between thermodynamic recovery from microscopic adiabatic recovery by analyzing how population transfer is redistributed toward energetically less costly channels rather than suppressed, using the thermally weighted spectral susceptibility to identify dynamically active regions.

4. Optimization of control parameters: The system can determine optimal stroke duration and rate allocation by identifying where the high-susceptibility schedule changes the work systematically and improving cycle performance from -6.98 x 10-4J to +3.12 x 10-3J at a specific driving rate.

5. Robustness assessment across system sizes: The improved AI can assess the stability of thermodynamic results by observing finite-size persistence, noting that the work-distribution width is close to 0.244J and that the majority-positive and positive-mean criteria retain the same ordering across Fibonacci sizes.

6. Multi-scale analysis of dynamical limits: The AI can distinguish between different dynamic regimes by analyzing how response changes across limits, such as how the extended, near-critical, and crossing protocols exchange their fluctuation ordering between the slow-driving, finite-rate, and state-frozen regimes.

Quasiperiodic systems combine sharply different spectral and localisation regimes with a dense hierarchy of dynamical time scales. We show that a finite-rate quantum Otto cycle can use this structure as a thermodynamic probe, revealing which parts of the spectrum become dynamically accessible and thermodynamically relevant during a driven transformation. For a generalised Aubry-André-Harper chain, the resulting response is not determined by the static quasiperiodic regime alone: extended, near-critical, and crossing protocols do not exhibit universal ordering of work fluctuations. Instead, the statistics reflect transition pathways that are simultaneously dynamically coupled, thermally occupied, and energetically significant. The same spectral accessibility separates thermodynamic recovery from microscopic adiabatic recovery. Positive mean work can reappear while the population transfer dynamics remain strongly nonadiabatic because finite-rate population transfer is redistributed toward energetically less costly channels rather than suppressed. The full work distribution reveals a further separation, with a finite rate window in which positive-work cycles form a majority although the mean work remains negative. This behaviour persists in finite-size analysis. A thermally weighted spectral susceptibility connects these effects to a distributed hierarchy of dynamically active spectral regions rather than to a single minimum-gap bottleneck. Finite thermal contacts preserve this picture while introducing a second time scale and intercycle memory. Quantum Otto cycles can therefore provide a fluctuation-resolved thermodynamic probe of quasiperiodic spectral accessibility, complementary to direct spectroscopic and eigenstate-resolved diagnostics.