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REVIEW 2 major objections 5 minor 74 references

Harnessing higher-dimensional fluctuations in an information engine

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read In d dimensions, an information engine's power saturates at $d-1$ (in units of $k_B T/\tau_r$) by feedback-cooling the transverse degrees of freedom, and a single transverse measurement matches the full engine at large gravitational loads.

desk verdict A genuinely new d-dimensional extension of the information engine, with a clean physical message about transverse feedback cooling; the main soft spots are an Eq. (13) prefactor issue and an unproven global optimality claim for the greedy rule in d>1. read the letter →

arxiv 2507.15503 v3 pith:PO5UYTRZ submitted 2025-07-21 cond-mat.stat-mech

Antonio Patrón Castro , John Bechhoefer , David A. Sivak This is my paper · ORCID
classification cond-mat.stat-mech PACS 05.40.-a05.70.Ln
keywords informationenginefeedbackcoolinghigher-dimensionalfluctuationsstochasticthermodynamicsBrownianmotorMaxwelldemonSzilardpowersaturation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper generalizes the one-dimensional information engine---an optically trapped Brownian bead that lifts a weight against gravity---to $d$ spatial dimensions. It shows that thermal fluctuations perpendicular to gravity, previously ignored, are the dominant resource: in the high-sampling-frequency limit the output power is $P_{\rm HF}^{\rm net}(\delta_g) = (d-1)\,\delta_g\, Z_{d-1}(\delta_g)/Z_d(\delta_g)$, which saturates to $d-1$ (in units of $k_B T/\tau_r$) as the gravitational force grows. Each transverse degree of freedom is feedback-cooled and extracts the maximum heat available per dimension, while the vertical degree of freedom satisfies the zero-work constraint and stores the extracted energy. Even a single transverse measurement, with no vertical measurement at all, reproduces the same asymptotic performance, so the engine's power is set by how many transverse dimensions are measured and harnessed.

What carries the argument

The zero-work optimal feedback rule (Eq. 10): after measuring the bead at $r_{n+1}$, the trap center is placed at $\lambda_{n+1+} = r_{n+1} + |r_{n+1} - \lambda_{n+}|\,\hat{z}$, the top of the hypersphere of radius $|r_{n+1} - \lambda_{n+}|$ centered on the bead. This single rule enforces exactly zero work per step, stores the maximum gravitational free energy per step, and splits the dynamics into a vertical component that stores energy and $d-1$ transverse components that follow a feedback-cooling protocol extracting all available heat. In the high-sampling-frequency limit, this reduces the engine to a Langevin-like description whose partition function $Z_d(\delta_g)$ yields the closed-form power formula.

What would settle it

Simulate or experimentally implement the $d=2$ engine and compare the steady-state average vertical velocity $\langle v_z \rangle$ against the prediction $P_{\rm net} = \delta_g \langle v_z \rangle = \delta_g\, Z_1(\delta_g)/Z_2(\delta_g)$ at sampling frequency $f_s \gg 1$. If the measured power falls short of $d-1$ for large $\delta_g$, or if a transverse-only (partial) engine fails to match the complete engine's asymptotic power, the central claim fails. Alternatively, a dynamic-programming search over feedback policies in $d=2$ that finds a policy with higher long-run power than the greedy rule (10) would falsify the optimality assumption.

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Extended reading notes

Core claim

The central claim is that a $d$-dimensional pure information engine achieves maximum output power $P_{\rm HF}^{\rm net}(\delta_g) = (d-1)\,\delta_g\, Z_{d-1}(\delta_g)/Z_d(\delta_g)$ in the high-sampling-frequency limit, where $Z_d(\delta_g) \equiv \int_0^\infty dL\, L^{d-1} e^{-L^2/2 + \delta_g L}$. As $\delta_g \to \infty$, this power asymptotes to $d-1$, meaning the engine extracts the maximum possible heat from each of the $d-1$ transverse degrees of freedom, each contributing one unit of $k_B T/\tau_r$. The mechanism is feedback cooling: after each measurement the trap center is moved to the top of the zero-work hypersphere centered on the bead, so every transverse fluctuation, regardless of its size, is exploited to lift the trap, while the vertical motion stores the extracted energy as gravitational potential energy. In the large-load limit vertical fluctuations become irrelevant, and an engine that measures only the transverse coordinates achieves the same asymptotic power.

Load-bearing premise

The feedback rule is chosen to maximize stored free energy in one step, and the paper assumes this greedy policy also maximizes long-run power and velocity in $d>1$ dimensions; if a non-greedy policy performs better over many cycles, the claimed power bounds and the comparison between engines could change.

Editorial extensions

If this is right

  • In $d>1$, output power no longer peaks at an intermediate load: it increases with $\delta_g$ and saturates at $d-1$ (in units of $k_B T/\tau_r$), so stronger opposing forces do not shut down the engine.
  • Each transverse degree of freedom adds one unit of power, so a three-dimensional version of the engine should show saturation at 2 units of $k_B T/\tau_r$, a clean scaling prediction.
  • An engine that ignores vertical measurements matches the full engine's asymptotic performance, making the partial engine more information-efficient for the same heat extraction.
  • The modular split---transverse fluctuations are harvested, vertical motion stores energy---mirrors the Szilard engine and gives a design principle for nanoscale energy harvesters.
  • At a fixed load $\delta_g \approx 0.8$, moving from $d=1$ to $d=2$ roughly doubles the output power, so dimensionality itself is a performance knob.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The greedy one-step policy's global optimality in $d>1$ is an open question; if a non-greedy policy outperforms it at finite $\delta_g$, formula (13) would be a lower bound on the true maximum power, though the $d-1$ saturation ceiling would likely survive.
  • The information-theoretic cost of the measurements is not included in the model; adding a cost per measurement would favor the partial (transverse-only) engine even more and may shift the optimal sampling frequency and load.
  • By analogy with reaction-coordinate selection, one could test whether measuring a tilted or rotated combination of transverse coordinates improves partial-engine performance beyond the axis-aligned $x$ measurement.
  • The prediction that power saturates at $d-1$ for large $\delta_g$ is a sharp experimental target: a 3D optical-trap realization should show saturation at 2 units of $k_B T/\tau_r$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This Letter generalizes the one-dimensional information engine of Saha et al. to d dimensions. The bead moves in a d-dimensional harmonic trap with a gravitational force along one axis. The trap-center feedback rule is chosen to do zero work on the bead and to maximize the stored gravitational free energy per measurement. The authors derive, with derivations deferred to the Supplemental Material, the steady-state output power in the high-sampling-frequency limit, P_HF_net(δg) = (d−1)δg Z_{d−1}(δg)/Z_d(δg), show that as δg→∞ this saturates to d−1 (in units of k_BT/τ_r), and interpret the enhancement as feedback cooling of the d−1 transverse degrees of freedom. They also introduce a 'partial' engine that measures only transverse components and achieves the same large-δg power. The paper concludes that higher-dimensional fluctuations are a valuable resource and that measurement degrees of freedom can be modularized relative to energy storage.

Significance. If the claims are fully supported, the result is a conceptually clean and quantitatively sharp extension of the information-engine paradigm. The analytical formula (13), the asymptotic saturation to d−1, and the close connection to feedback cooling are concrete and falsifiable; the partial-engine result (16) suggests a design principle for reducing measurement overhead. The availability of openly available codes is a positive feature. However, the strength of the contribution depends on two points: the d→1 limiting behavior of the central formula, and whether the greedy feedback rule is truly optimal for long-run power in d>1. Neither is established in the main text.

major comments (2)
  1. [Optimal performance, Eq. (13)] The text states that 'Equation (13) holds even for d→1, recovering the d=1 expression for the output power from [47].' As written, Eq. (13) is not meaningful at d=1 because the prefactor (d−1) vanishes while Z_{d−1}=Z_0 is not defined by Eq. (14), whose measure L^{d−1}dL would require L^{-1}dL for d=1. If the intended statement is a limit from d>1, the limiting procedure must be shown explicitly, including the regularization of Z_0 and the demonstration that the limit reproduces the known 1D expression. This is load-bearing because the paper's comparisons between d=2 and d=1 and the phrase 'recovering the d=1 expression' depend on this limit.
  2. [Optimal performance, feedback rule (10) and Conclusions] The feedback rule (10) is derived by maximizing the per-step stored free energy subject to the zero-work constraint W_{n+1}=0. The paper's abstract and title use the phrase 'optimal performance', and the Conclusions state that the engine 'extracts the maximum possible power from the d−1 transverse degrees of freedom.' For d=1, Ref. [47] proves that this greedy rule also maximizes long-run power and velocity. No analogous proof is given for d>1. In a higher-dimensional state space, a non-greedy zero-work rule could in principle sacrifice immediate gain to shape the steady-state distribution of the relative vector and yield larger long-run power. Without such a proof (or a numerical search over zero-work policies), Eqs. (13), (16), and Figs. 3–4 are properties of the specific greedy protocol, not necessarily of the optimal engine. The authors should either supply the missing optimality argument or qualify the claims to 'optimal within the class of one-step-greedy zero-work rules.'
minor comments (5)
  1. [Optimal performance, Eq. (13)] The sentence 'Equation (13) holds even for d→1' is ambiguous because the limit is not defined; please replace it with a precise statement and, if possible, a one-line derivation of the limit.
  2. [Eqs. (11) and (15)] The notation 'n++1' for the post-update index is unconventional and could be misread as a double increment; consider using a distinct symbol or a clearer convention such as n+ after update.
  3. [Fig. 4] The caption states that the dotted lines are 'asymptotic limit d−1 for δ_g→∞', and the inset mentions analytic forms, but it does not specify the algebraic form of the dotted lines; please state the asymptotic expression (e.g., (d−1)/δ_g) explicitly.
  4. [Data availability] Reference [73] is incomplete: it lists only 'A. Patrón Castro, (2025), GitHub repository' without a URL or repository identifier.
  5. [Partial information engine, Eq. (15)] The term 'pure information engine' is used for the partial engine where only the average work is zero; this differs from the complete engine where W_{n+1}=0 at every step. Please clarify that the zero-work condition is imposed only in an average sense for the partial engine.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the d-dimensional power formula is derived from the stated model and feedback rule, not fitted into existence or reduced to a self-citation.

full rationale

The paper's central quantitative result, Eq. (13), is an analytic high-sampling-frequency limit derived from the discrete-time dynamics (5), the zero-work condition, and the explicit feedback rule (10). The feedback rule itself is derived in the text from two stated design conditions: zero work per trap movement and maximization of stored free energy. This is an input choice, not a fitted parameter disguised as a prediction. The asymptotic saturation to d-1 follows from Laplace's method applied to the partition function (14), an independent mathematical step. The comparison to feedback cooling cites an external result [50] and does not define the engine's power into existence; rather, it interprets the already-derived saturation. Self-citations such as [47] are used for the d=1 baseline, the choice delta_g = 0.8, and the precedent for the feedback rule, but the d>1 derivation does not reduce to those citations: the rule is re-derived and the high-frequency power is computed from the model's steady-state statistics. The concern that the greedy one-step rule is not proven globally optimal for d>1 is a correctness or scope-of-claim issue, not circularity, because the derived formulas remain valid properties of the explicit rule (10) irrespective of global optimality. No load-bearing argument is equivalent, by construction, to its own inputs. Therefore the paper exhibits no significant circularity.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The model introduces no new physical entities. Its load-bearing inputs are the overdamped, noiseless-measurement idealization, the greedy feedback policy, and prior results on feedback cooling and the d=1 engine.

free parameters (1)
  • δ_g (dimensionless gravitational force) = 0.8 (used for Fig. 3; from prior d=1 optimization, not fitted here)
    A physical parameter of the model quantifying gravity relative to thermal force; chosen for the comparison figures, varied in Fig. 4. It is not fitted to data in this paper.
assumptions (6)
  • domain assumption Overdamped Langevin dynamics with isotropic harmonic trap and gravitational force (Eq. 1).
    The entire engine dynamics are modeled as overdamped Brownian motion; inertial effects and measurement noise are neglected.
  • domain assumption Measurements are exact and instantaneous, with immediate trap updates (Eq. 5).
    The feedback loop assumes noiseless discrete-time measurements of the bead position; the paper notes information costs are deferred to future work.
  • ad hoc to paper The greedy one-step feedback rule (10), maximizing per-step free-energy storage under zero work, is globally optimal for long-run power and velocity in d>1.
    The paper follows the d=1 construction from Ref. [47] but does not prove global optimality of this policy in higher dimensions.
  • domain assumption In the high-sampling-frequency limit, trap-center dynamics can be approximated by a continuous Langevin-like equation that yields the partition-function formula (13).
    Used to derive the analytic high-frequency power; the discrete-time process is replaced by a continuous approximation that must be justified in the limit t_s→0.
  • domain assumption Feedback cooling extracts a maximum power of 1 per independent degree of freedom, from Ref. [50].
    The d-1 saturation bound relies on this prior result for the maximum heat extraction rate per cooled dimension.
  • domain assumption A steady-state distribution exists for the relative bead-trap displacements used to define the partial engine's average-zero-work rule (15).
    The averages in Eq. (15) are taken over the steady-state distribution; existence and uniqueness are assumed.

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Cite this review

Pith. "Pith review of Harnessing higher-dimensional fluctuations in an information engine." pith.science (2026). https://pith.science/paper/PO5UYTRZ

@misc{pith2026250715503,
  author       = {Pith},
  title        = {Pith review of: Harnessing higher-dimensional fluctuations in an information engine},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PO5UYTRZ}},
  note         = {Machine review of arXiv:2507.15503}
}
abstract

We study the optimal performance of an information engine consisting of an overdamped Brownian bead confined in a controllable, $d$-dimensional harmonic trap and additionally subjected to gravity. The trap's center is updated dynamically via a feedback protocol designed such that no external work is done by the trap on the bead, while maximizing the extraction of gravitational potential energy and achieving directed motion. We show that performance strikingly improves when thermal fluctuations in directions perpendicular to gravity are harnessed. This improvement arises from feedback cooling of these transverse degrees of freedom, along which all heat is extracted; comparable performance can be achieved even without vertical measurements. This engine design modularizes the functions of harnessing fluctuations and storing free energy, drawing a close analogy to the Szilard engine.

Figures

Figures reproduced from arXiv: 2507.15503 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Information-engine output power [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Output power (a) and vertical velocity (b) as functions [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Reference graph

Works this paper leans on

74 extracted references · 68 canonical work pages

  1. [47]

    toddimensions and find striking increases in the rate of energy extraction and related measures of performance. We show that the performance enhancement results from feed- back cooling of thermal fluctuations along the transverse de- grees of freedom, thereby extractingallavailable heat, since all such fluctuations are favorable. We demonstrate that feed-...

    work page Pith review arXiv 2026

  2. [1]

    C. G. Knott,Life and Scientific Work of Peter Guthrie Tait (Cambridge University Press, London, 1911)

    work page 1911

  3. [2]

    Szilard, Über die entropieverminderung in einem thermody- namischen system bei eingriffen intelligenter wesen, Z

    L. Szilard, Über die entropieverminderung in einem thermody- namischen system bei eingriffen intelligenter wesen, Z. Angew. Phys.53, 840 (1929)

    work page 1929

  4. [3]

    Szilard, On the decrease of entropy in a thermodynamic sys- tem by the intervention of intelligent beings, Behav

    L. Szilard, On the decrease of entropy in a thermodynamic sys- tem by the intervention of intelligent beings, Behav. Sci.9, 301 (1964)

    work page 1964

  5. [4]

    Landauer, Irreversibility and heat generation in the comput- ing process, IBM J

    R. Landauer, Irreversibility and heat generation in the comput- ing process, IBM J. Res. Dev.5, 183 (1961)

    work page 1961

  6. [5]

    C. H. Bennett, The thermodynamics of computation—a review, Int. J. Theor. Phys.21, 905 (1982)

    1982

  7. [6]

    Sekimoto, Kinetic characterization of heat bath and the en- ergetics of thermal ratchet models, J

    K. Sekimoto, Kinetic characterization of heat bath and the en- ergetics of thermal ratchet models, J. Phys. Soc. Jpn.66, 1234 (1997)

    work page 1997

  8. [7]

    Sekimoto,Stochastic Energetics, Lecture Notes in Physics, V ol

    K. Sekimoto,Stochastic Energetics, Lecture Notes in Physics, V ol. 799 (Springer, 2010)

    work page 2010

Show all 74 references
  1. [8]

    Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep

    U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys.75, 126001 (2012)

    2012

  2. [9]

    C. V . den Broeck and M. Esposito, Ensemble and trajec- tory thermodynamics: A brief introduction, Physica A418, 6 (2015)

    2015

  3. [10]

    Seifert,Stochastic Thermodynamics(Cambridge University Press, 2025)

    U. Seifert,Stochastic Thermodynamics(Cambridge University Press, 2025)

    2025

  4. [11]

    Toyabe, T

    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental demonstration of information-to-energy conver- sion and validation of the generalized Jarzynski equality, Nat. Phys.6, 988 (2010)

    2010

  5. [12]

    P. A. Camatiet al., Experimental rectification of entropy pro- duction by Maxwell’s demon in a quantum system, Phys. Rev. Lett.117, 240502 (2016)

    2016

  6. [13]

    J. V . Koski, A. Kutvonen, I. M. Khaymovich, T. Ala-Nissila, and J. P. Pekola, On-chip Maxwell’s demon as an information- powered refrigerator, Phys. Rev. Lett.115, 260602 (2015)

    2015

  7. [14]

    Cottetet al., Observing a quantum Maxwell demon at work, Proc

    N. Cottetet al., Observing a quantum Maxwell demon at work, Proc. Natl. Acad. Sci. U.S.A.114, 7561 (2017)

    2017

  8. [15]

    Masuyamaet al., Information-to-work conversion by Maxwell’s demon in a superconducting circuit quantum elec- trodynamical system, Nat

    Y . Masuyamaet al., Information-to-work conversion by Maxwell’s demon in a superconducting circuit quantum elec- trodynamical system, Nat. Commun.9, 1291 (2018)

    2018

  9. [16]

    J. V . Koski, V . F. Maisi, J. P. Pekola, and D. V . Averin, Exper- imental realization of a Szilard engine with a single electron, Proc. Natl. Acad. Sci. U.S.A.111, 13786 (2014)

    2014

  10. [17]

    Chida, S

    K. Chida, S. Desai, K. Nishiguchi, and A. Fujiwara, Power gen- erator driven by Maxwell’s demon, Nat. Commun.8, 15310 (2017)

    2017

  11. [18]

    Admon, S

    T. Admon, S. Rahav, and Y . Roichman, Experimental realiza- tion of an information machine with tunable temporal correla- tions, Phys. Rev. Lett.121, 180601 (2018)

    2018

  12. [19]

    Goerlich, L

    R. Goerlich, L. Hoek, O. Chor, S. Rahav, and Y . Roichman, Ex- perimental realizations of information engines: Beyond proof of concept, Europhys. Lett.149, 61001 (2025)

    2025

  13. [20]

    Baldovin, I

    M. Baldovin, I. Ben Yedder, C. A. Plata, D. Raynal, L. Rondin, E. Trizac, and A. Prados, Optimal control of levitated nanopar- ticles through finite-stiffness confinement, Phys. Rev. Lett.135, 097102 (2025)

    2025

  14. [21]

    Bérutet al., Experimental verification of Landauer’s princi- ple linking information and thermodynamics, Nature483, 187 (2012)

    A. Bérutet al., Experimental verification of Landauer’s princi- ple linking information and thermodynamics, Nature483, 187 (2012)

    2012

  15. [22]

    Y . Jun, M. Gavrilov, and J. Bechhoefer, High-precision test of Landauer’s principle in a feedback trap, Phys. Rev. Lett.113, 190601 (2014)

    2014

  16. [23]

    J. V . Koski, V . F. Maisi, T. Sagawa, and J. P. Pekola, Experimen- tal observation of the role of mutual information in the nonequi- librium dynamics of a Maxwell demon, Phys. Rev. Lett.113, 6 030601 (2014)

    2014

  17. [24]

    J. Hong, B. Lambson, D. Scott, and J. Bokor, Experimental test of Landauer’s principle in single-bit operations on nanomag- netic memory bits, Sci. Adv.2, e1501492 (2016)

    2016

  18. [25]

    Ciliberto, Landauer’s Bound and Maxwell’s Demon, inIn- formation Theory: Poincaré Seminar 2018, edited by B

    S. Ciliberto, Landauer’s Bound and Maxwell’s Demon, inIn- formation Theory: Poincaré Seminar 2018, edited by B. Du- plantier and V . Rivasseau (Springer International Publishing, Cham, 2021) pp. 87–112

    2018

  19. [26]

    S. Dago, J. Pereda, N. Barros,et al., Information and thermo- dynamics: fast and precise approach to Landauer’s bound in an underdamped micromechanical oscillator, Phys. Rev. Lett.126, 170601 (2021)

    2021

  20. [27]

    Archambault, C

    A. Archambault, C. Crauste-Thibierge, A. Imparato, C. Jarzyn- ski, S. Ciliberto, and L. Bellon, Information engine fueled by first-passage times, Phys. Rev. Lett.135, 147101 (2025)

    2025

  21. [28]

    T. Li, S. Kheifets, and M. G. Raizen, Millikelvin cooling of an optically trapped microsphere in vacuum, Nat. Phys.7, 527 (2011)

    2011

  22. [29]

    Gieseler, B

    J. Gieseler, B. Deutsch, R. Quidant,et al., Subkelvin paramet- ric feedback cooling of a laser-trapped nanoparticle, Phys. Rev. Lett.109, 103603 (2012)

    2012

  23. [30]

    Tebbenjohanns, M

    F. Tebbenjohanns, M. Frimmer, A. Militaru,et al., Cold damp- ing of an optically levitated nanoparticle to microkelvin tem- peratures, Phys. Rev. Lett.122, 223601 (2019)

    2019

  24. [31]

    Barros, S

    N. Barros, S. Ciliberto, and L. Bellon, Probabilistic work ex- traction on a classical oscillator beyond the second law, Phys. Rev. Lett.133, 057101 (2024)

    2024

  25. [32]

    Paneru, S

    G. Paneru, S. Dutta, T. Tlusty, and H. K. Pak, Reaching and vi- olating thermodynamic uncertainty bounds in information en- gines, Phys. Rev. E102, 032126 (2020)

    2020

  26. [33]

    Klinger and G

    J. Klinger and G. M. Rotskoff, Universal energy-speed- accuracy trade-offs in driven nonequilibrium systems, Phys. Rev. E111, 014114 (2025)

    2025

  27. [34]

    Serreli, C

    V . Serreli, C. Lee, E. R. Kay,et al., A molecular information ratchet, Nature445, 523 (2007)

    2007

  28. [35]

    M. P. Leighton and D. A. Sivak, Inferring subsystem efficien- cies in bipartite molecular machines, Phys. Rev. Lett.130, 178401 (2023)

    2023

  29. [36]

    M. P. Leighton, J. Ehrich, and D. A. Sivak, Information arbi- trage in bipartite heat engines, Phys. Rev. X14, 041038 (2024)

    2024

  30. [37]

    M. P. Leighton and D. A. Sivak, Flow of energy and information in molecular machines, Annu. Rev. Phys. Chem.76, 379–403 (2025), review article; arXiv preprint available

    2025

  31. [38]

    Tsuruyama, Rna polymerase is a unique Maxwell’s demon that converts its transcribing genetic information to free energy for its movement, Eur

    T. Tsuruyama, Rna polymerase is a unique Maxwell’s demon that converts its transcribing genetic information to free energy for its movement, Eur. Phys. J. Plus138, 1 (2023)

    2023

  32. [39]

    J. M. R. Parrondo, J. M. Horowitz, and T. Sagawa, Thermody- namics of information, Nature Phys.11, 131 (2015)

    2015

  33. [40]

    du Buisson, D

    J. du Buisson, D. A. Sivak, and J. Bechhoefer, Performance lim- its of information engines, Adv. Phys.: X9, 2352112 (2024), publisher: Taylor & Francis

    2024

  34. [41]

    J. N. E. Lucero, J. Ehrich, J. Bechhoefer,et al., Maximal fluctu- ation exploitation in gaussian information engines, Phys. Rev. E104, 044122 (2021)

    2021

  35. [42]

    T. K. Saha and J. Bechhoefer, Optical trapping and optical mi- cromanipulation, inProc. SPIE Int. Soc. Opt. Eng., V ol. 11798 (SPIE, 2021) pp. 53–61

    2021

  36. [43]

    T. K. Saha, J. N. E. Lucero, J. Ehrich,et al., Bayesian informa- tion engine that optimally exploits noisy measurements, Phys. Rev. Lett.129, 130601 (2022)

    2022

  37. [44]

    T. K. Saha, J. Ehrich, M. Gavrilov,et al., Information engine in a nonequilibrium bath, Phys. Rev. Lett.131, 057101 (2023)

    2023

  38. [45]

    Paneru, S

    G. Paneru, S. Dutta, and H. K. Pak, Colossal power extrac- tion from active cyclic Brownian information engines, J. Phys. Chem. Lett.13, 6912 (2022)

    2022

  39. [46]

    Paneru, D

    G. Paneru, D. Y . Lee, J.-M. Park, J. T. Park, J. D. Noh, and H. K. Pak, Optimal tuning of a Brownian information engine operating in a nonequilibrium steady state, Phys. Rev. E98, 052119 (2018)

    2018

  40. [48]

    T. K. Saha, J. N. E. Lucero, J. Ehrich, D. A. Sivak, and J. Bech- hoefer, Maximizing power and velocity of an information en- gine, Proc. Natl. Acad. Sci. U.S.A.118, e2023356118 (2021)

    2021

  41. [49]

    P. E. Kloeden and E. Platen,Numerical Solution of Stochas- tic Differential Equations(Springer Berlin Heidelberg, Berlin, Heidelberg, 1992)

    1992

  42. [50]

    [47, 48, 51]

    See Supplemental Material for details of the derivations and nu- merical methods, which includes Refs. [47, 48, 51]

  43. [51]

    D. Y . Lee, J. Um, G. Paneru, and H. K. Pak, An experimentally- achieved information-driven Brownian motor shows maximum power at the relaxation time, Scientific Reports8, 12121 (2018)

    2018

  44. [52]

    C. M. Bender and S. A. Orszag,Advanced Mathematical Meth- ods for Scientists and Engineers(McGraw-Hill, 1978)

    1978

  45. [53]

    Roldán, I

    E. Roldán, I. A. Martínez, J. M. R. Parrondo, and D. Petrov, Universal features in the energetics of symmetry breaking, Na- ture Physics10, 457 (2014)

    2014

  46. [54]

    Ma and H

    A. Ma and H. Li, Reaction Coordinates Are Optimal Channels of Energy Flow, Annu. Rev. Phys. Chem.76, 153 (2025)

    2025

  47. [55]

    M. D. Louwerse and D. A. Sivak, Information thermodynamics of the transition-path ensemble, Phys. Rev. Lett.128, 170602 (2022)

    2022

  48. [56]

    Kolchinsky, I

    A. Kolchinsky, I. Marvian, C. Gokler, Z.-W. Liu, P. Shor, O. Shtanko, K. Thompson, D. Wolpert, and S. Lloyd, Maximiz- ing free energy gain, Entropy27, 10.3390/e27010091 (2025)

    2025 doi

  49. [57]

    Lucente, A

    D. Lucente, A. Manacorda, A. Plati, A. Sarracino, and M. Bal- dovin, Optimal control of an electromechanical energy har- vester (2025), arXiv:2501.07735 [cond-mat.stat-mech]

    2025 arXiv

  50. [58]

    K. S. Olsen, R. Goerlich, Y . Roichman, and H. Löwen, Harness- ing non-equilibrium forces to optimize work extraction, Nat. Commun.16, 11031 (2025)

    2025

  51. [59]

    Ribezzi-Crivellari and F

    M. Ribezzi-Crivellari and F. Ritort, Large work extraction and the Landauer limit in a continuous Maxwell demon, Nat. Phys. 15, 660 (2019)

    2019

  52. [60]

    Paneru, D

    G. Paneru, D. Y . Lee, T. Tlusty, and H. K. Pak, Lossless Brow- nian information engine, Phys. Rev. Lett.120, 020601 (2018)

    2018

  53. [61]

    Still, Thermodynamic cost and benefit of memory, Phys

    S. Still, Thermodynamic cost and benefit of memory, Phys. Rev. Lett.124, 050601 (2020)

    2020

  54. [62]

    Dago and L

    S. Dago and L. Bellon, Dynamics of information erasure and extension of Landauer’s bound to fast processes, Phys. Rev. Lett.128, 070604 (2022)

    2022

  55. [63]

    S. Dago, S. Ciliberto, and L. Bellon, Adiabatic computing for optimal thermodynamic efficiency of information processing, Proc. Natl. Acad. Sci. U.S.A.120, e2301742120 (2023)

    2023

  56. [64]

    Archambault, C

    A. Archambault, C. Crauste-Thibierge, S. Ciliberto, and L. Bel- lon, Inertial effects in discrete sampling information engines, Europhys. Lett.148, 41002 (2024)

    2024

  57. [65]

    Sanders, M

    J. Sanders, M. Baldovin, and P. Muratore-Ginanneschi, Optimal control of underdamped systems: An analytic approach, J. Stat. Phys.191, 117 (2024)

    2024

  58. [66]

    Sanders, M

    J. Sanders, M. Baldovin, and P. Muratore-Ginanneschi, Mini- mal work protocols for inertial particles in nonharmonic traps, Phys. Rev. E111, 034127 (2025)

    2025

  59. [67]

    Bechhoefer,Control Theory for Physicists(Cambridge Uni- versity Press, Cambridge, United Kingdom, 2021)

    J. Bechhoefer,Control Theory for Physicists(Cambridge Uni- versity Press, Cambridge, United Kingdom, 2021)

    2021

  60. [68]

    K. H. Kim and H. Qian, Entropy production of Brownian macromolecules with inertia, Phys. Rev. Lett.93, 120602 (2004)

    2004

  61. [69]

    Malgaretti and H

    P. Malgaretti and H. Stark, Szilard engines and information- based work extraction for active systems, Phys. Rev. Lett.129, 7 228005 (2022)

    2022

  62. [70]

    Cocconi and L

    L. Cocconi and L. Chen, Efficiency of an autonomous, dynamic information engine operating on a single active particle, Phys. Rev. E110, 014602 (2024)

    2024

  63. [71]

    Datta, P

    A. Datta, P. Pietzonka, and A. C. Barato, Second law for active heat engines, Phys. Rev. X12, 031034 (2022)

    2022

  64. [72]

    Lee, J.-M

    J. Lee, J.-M. Park, and H. Park, Brownian heat engine with ac- tive reservoirs, Phys. Rev. E102, 032116 (2020)

    2020

  65. [73]

    Garcia-Millan, J

    R. Garcia-Millan, J. Schüttler, M. E. Cates, and S. A. M. Loos, Optimal closed-loop control of active particles and a minimal information engine, Phys. Rev. Lett.135, 088301 (2025)

    2025

  66. [74]

    Patrón Castro, (2025), GitHub repository

    A. Patrón Castro, (2025), GitHub repository

    2025

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