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arXiv:2610.32683

Stochastic and quantum autonomous information machine: efficiency fluctuations, precision and optimization

Lucas Trigal, Gonzalo Manzano

cond-mat.stat-mechquant-phSubmitted Oct 23, 2026• Announced Oct 26, 2026
arXivHTMLPDF

Abstract

We investigate the conversion between thermal and informational resources in an autonomous machine coupled to thermal reservoirs and a tape, playing the role of an information reservoir. The machine is able to perform information erasure driven by heat, and information-powered refrigeration, for which we introduce suitable efficiency definitions. We focus on the role of fluctuations in the currents and stochastic efficiencies, as well as in operation at optimal performance. The model is also extended to allow a coherent information reservoir, which is able to modify operation and performance. All in all, our work provides insights for the design and optimization of information-to-work conversion devices at small scales.

AI Summary

The paper studies fluctuations and optimal performance in an autonomous machine that converts thermal gradients into information erasure, or consumes an ordered bit stream to refrigerate a cold bath. The model consists of two equal-gap two-level systems coupled to hot and cold reservoirs, with Poisson-distributed tape interactions coupling the machine’s degenerate single-excitation states without exchanging energy. A four-state Markov generator, full counting statistics and large-deviation methods characterize stationary currents and efficiencies. Operation is controlled by the tape bias $\delta_{\rm tape}=\ln(p_0/p_1)$ relative to $\delta_{\rm th}=(\beta_c-\beta_h)\Delta E$: positive biases below the thermal bias produce erasure, while larger biases produce refrigeration. The erasure efficiency obeys $\bar\eta\leq1-\beta_h/\beta_c$; the refrigerator COP, including a tape-reset contribution, satisfies $\bar\epsilon/\epsilon_C=\delta_{\rm th}/\delta_{\rm tape}\leq1$. Reversible operation has vanishing currents. Erasure’s stochastic entropy output lacks the time-reversal antisymmetry needed to single out Carnot efficiency as least probable, whereas tight coupling suppresses long-time COP fluctuations. Energy-gap optimization yields power–efficiency trade-offs and half-Carnot limits in the specified weak-driving regimes. A coherent-qubit tape extension, treated using a weak-collision quantum master equation, predominantly expands dissipative operation and reduces current precision at fixed tape populations in the parameter regime studied. The analysis assumes fresh, independent tape elements, weak collisions and steady-state operation; the variance-crossing result additionally requires slow effective tape coupling. Correlated tapes and multicycle machines are left for future study, and experimental implementations are proposed rather than demonstrated.

Little sign of AI-generated textIncrementalPossible error

Error found: The quantum extension calls its interaction energy-preserving, but its nondegenerate tape Hamiltonian and degenerate machine transition give [H_m + H_tape, H_int] ≠ 0, requiring a corrected Hamiltonian or additional energy accounting. The logarithmic entropy expansion used to discuss nearly pure incoming tape states is nonuniform at the pure-state boundary, where the exact entropy-change rate remains bounded by r ln 2.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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20 pages, 7 figures

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We investigate the conversion between thermal and informational resources in an autonomous machine coupled to thermal reservoirs and a tape, playing the role of an information reservoir. The machine is able to perform information erasure driven by heat, and information-powered refrigeration, for which we introduce suitable efficiency definitions. We focus on the role of fluctuations in the currents and stochastic efficiencies, as well as in operation at optimal performance. The model is also extended to allow a coherent information reservoir, which is able to modify operation and performance. All in all, our work provides insights for the design and optimization of information-to-work conversion devices at small scales.
The paper studies fluctuations and optimal performance in an autonomous machine that converts thermal gradients into information erasure, or consumes an ordered bit stream to refrigerate a cold bath. The model consists of two equal-gap two-level systems coupled to hot and cold reservoirs, with Poisson-distributed tape interactions coupling the machine’s degenerate single-excitation states without exchanging energy.
A four-state Markov generator, full counting statistics and large-deviation methods characterize stationary currents and efficiencies. Operation is controlled by the tape bias δtape=ln⁡(p0/p1)\delta_{\rm tape}=\ln(p_0/p_1)δtape​=ln(p0​/p1​) relative to δth=(βc−βh)ΔE\delta_{\rm th}=(\beta_c-\beta_h)\Delta Eδth​=(βc​−βh​)ΔE: positive biases below the thermal bias produce erasure, while larger biases produce refrigeration. The erasure efficiency obeys ηˉ≤1−βh/βc\bar\eta\leq1-\beta_h/\beta_cηˉ​≤1−βh​/βc​; the refrigerator COP, including a tape-reset contribution, satisfies ϵˉ/ϵC=δth/δtape≤1\bar\epsilon/\epsilon_C=\delta_{\rm th}/\delta_{\rm tape}\leq1ϵˉ/ϵC​=δth​/δtape​≤1. Reversible operation has vanishing currents. Erasure’s stochastic entropy output lacks the time-reversal antisymmetry needed to single out Carnot efficiency as least probable, whereas tight coupling suppresses long-time COP fluctuations.
Energy-gap optimization yields power–efficiency trade-offs and half-Carnot limits in the specified weak-driving regimes. A coherent-qubit tape extension, treated using a weak-collision quantum master equation, predominantly expands dissipative operation and reduces current precision at fixed tape populations in the parameter regime studied.
The analysis assumes fresh, independent tape elements, weak collisions and steady-state operation; the variance-crossing result additionally requires slow effective tape coupling. Correlated tapes and multicycle machines are left for future study, and experimental implementations are proposed rather than demonstrated.
While externally driven information engines are well understood, the thermodynamic constraints of their autonomous counterparts remain an open question. Here, we investigate the finite-time operation of an autonomous machine functioning as both an information eraser and a refrigerator, revealing that its irreversibility is bounded by the transient information geometry. Beyond steady-state boundaries, we map the landscape of optimal operation times across both functional modes, uncovering a unique synergistic regime where erasure power PPP and efficiency ηηη increase simultaneously. Fundamentally, this performance is governed by a trade-off relation, v(1−η)P/η≤Dv(1-η)P/η\le Dv(1−η)P/η≤D, where vvv is the operational speed and DDD denotes an information-geometric distance. Our findings pave the way for optimizing fast autonomous information-energy conversion.
Quantum coherence has been shown to impact the operational capabilities of quantum systems performing thermodynamic tasks in a significant way, and yet the possibility and conditions for genuine coherence-enhanced thermodynamic operation remain unclear. Introducing a comparison with classical machines using the same set of thermodynamic resources, we show that for steady-state quantum thermal machines – both autonomous and externally driven – that interact weakly with thermal reservoirs and work sources, the presence of coherence induced by perturbations in the machine Hamiltonian guarantees a genuine thermodynamic advantage under mild conditions. This advantage applies to both cases where the induced coherence is between levels with different energies or between degenerate levels. On the other hand, we show that engines subjected to noise-induced coherence can be outperformed by classical stochastic engines using exactly the same set of (incoherent) resources. We illustrate our results with three prototypical models of heat engines and refrigerators: the three-level amplifier, the three-qubit autonomous refrigerator, and a noise-induced-coherence machine.
Abstract In the quest for high-performance quantum thermal machines, looking for an optimal thermodynamic efficiency is only part of the issue. Indeed, at the level of quantum devices, fluctuations become extremely relevant and need to be taken into account. In this paper we study the thermodynamic uncertainty relations for a quantum thermal machine with a quantum harmonic oscillator as a working medium, connected to two thermal baths, one of which is dynamically coupled. We show that parameters can be found such that the machine operates both as a quantum engine or refrigerator, with both sizeable efficiency and small fluctuations.
The study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.
Abstract The characterization and control of quantum effects in the performance of thermodynamic tasks may open new avenues for small thermal machines working in the nanoscale. We study the impact of coherence in the energy basis in the operation of a small thermal machine which can act either as a heat engine or as a refrigerator. We show that input coherence may enhance the machine performance and allow it to operate in otherwise forbidden regimes. Moreover, our results also indicate that, in some cases, coherence may also be detrimental, rendering optimization of particular models a crucial task for benefiting from coherence-induced enhancements.
We present core ideas of quantum thermodynamics and a simple model of continuous quantum heat engines, relating their efficiency to the fundamental limit set by the Second Law. We apply a probability current analysis to these systems, allowing us to better understand their steady state behavior. Finally, we introduce a simple quantum mechanical model of Maxwell’s Demon—a system that extracts energy from a thermal reservoir at the cost of writing information to its memory—and analyze its behavior for a range of possible reservoir and memory tape parameters. We find that the information efficiency of our system is bounded by Landauer’s Principle and that it can approach this bound when its thermal reservoir and memory tape are nearly equally mixed.