{"id":"b690f098-fc15-4a3e-92bc-311edb12de9c","arxiv_id":"2501.18613","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"For active particles dragged in a harmonic trap, closed-loop control with a single self-propulsion measurement reduces average external work and enables an information engine whose efficiency is bounded by 1/(4 ln2).","lead":"This paper derives exact minimum-work protocols for moving a harmonic trap containing an active particle, and shows that measuring the particle's self-propulsion once allows work to be extracted. It identifies when feedback beats open-loop control and proposes a minimal 'active information engine' with a theoretical efficiency bound.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed universal information-efficiency bound η≤1/(4 ln 2) rests on the ad hoc identification of the demon temperature with the active-noise coefficient Dv (Sec. IV D); if the thermal temperature D is used instead, the bound no longer holds and the reported efficiency values change.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern: the information efficiency and the 1/(4 ln 2) bound depend on the demon temperature being Dv. This is indeed the most fragile point in the central claim. The open-loop results and the external-work closed-loop optimization are internally consistent and carefully derived; the stress-test does not find an error in those derivations. However, the information-engine efficiency, which is a headline application, rests on an unmotivated identification of the demon temperature with the active-noise coefficient. The paper states this assumption explicitly in Sec. IV D but then presents Eq. (84) as a 'universal upper efficiency bound' in the conclusion, without prominently flagging that the bound is contingent on T = Dv. A concrete recalculation with T = D would likely remove the bound and could change the efficiency ordering in some parameter regimes. Because the concern is about the interpretation and generality of a central quantitative result, rather than a mathematical error in the external-work analysis, the appropriate disposition is conditional acceptance: the manuscript should be revised to state the T = Dv assumption prominently, discuss the T = D alternative, and adjust the claim of universality accordingly. The paper remains a solid and reproducible contribution for the external-work cost functional, which is why REJECT or UNVERDICTED would be too strong.","tokens_in":31122,"tokens_out":7106,"duration_ms":90162,"concrete_test":"Recompute the information efficiency in Eq. (82) and the bound in Eq. (84) using the thermal diffusion constant D from Eq. (2) as the demon temperature instead of Dv, keeping all other definitions fixed. If, for representative parameters (e.g., kτ = 1, tf/τ large, ε/ω = 0.1, and τω^2/D = 10), the RTP efficiency exceeds 1/(4 ln 2), or if the RTP/AOUP ordering changes, then the universal bound is not robust and the claim must be restated as conditional on T = Dv.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Equation (82) defines η using the information-acquisition cost Dv I[vm;vr], after Sec. IV D sets the demon temperature to T = Dv. This is an extra modeling assumption, not a consequence of the dynamics: the heat bath in Eq. (2) has temperature D, and the demon is not part of the model. The choice is consequential. Replacing Dv by D gives, for small ε, η_RTP ≈ (τ ω^2 Δw_engine)/(D ln 2) and η_AOUP → 0 because I_AOUP ~ 1/2 ln(1 + ω^2/ε^2) diverges. For fixed τ ω^2/D large, η_RTP can exceed 1/(4 ln 2), so Eq. (84) is not a universal bound but an artifact of the T = Dv normalization. The qualitative RTP-over-AOUP ordering may survive, but the headline quantitative bound and the efficiency values in Fig. 7 are not robust to this choice. This is a correctness-risk concern about the central information-engine claim, not merely a disagreement with consensus.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript studies the finite-time dragging of a harmonically trapped active particle in one dimension, comparing an Active Ornstein-Uhlenbeck particle (AOUP) and a run-and-tumble particle (RTP). The authors derive exact optimal trap-motion protocols for open-loop control and for closed-loop control based on a single initial measurement of the self-propulsion. They show that the open-loop optimal protocol and mean work coincide with the passive-particle result, while activity increases work fluctuations; that a self-propulsion measurement reduces the mean external work by an amount proportional to (omega^2 - epsilon^2) tau Delta w (Eq. (62)); and that the resulting active information engine has higher information efficiency for RTPs than for AOUPs, with a claimed upper bound eta <= 1/(4 ln 2) (Eq. (84)). An alternative cost functional that includes internal dissipation is analyzed in Sec. VI, where the closed-loop advantage disappears.","tokens_in":31302,"tokens_out":9995,"duration_ms":99254,"significance":"The analytic treatment is a clear strength: the Euler-Lagrange optimization, the work-variance computation, the measurement-uncertainty correction, and the total-work functional are all developed in closed form, with simulations supporting the work distributions. If the assumptions are accepted, the paper provides exact reference results for optimal control of active matter and a concrete demonstration that finite persistence time is beneficial under feedback. The main caveat is that the universal efficiency bound and the quoted efficiencies depend on assigning the information-acquisition cost a temperature T=Dv; this assumption is not derived from the model. The qualitative RTP-over-AOUP ordering may survive, but the quantitative headline result needs adjustment or justification.","major_comments":[{"comment":"The information-efficiency bound Eq. (84) rests on the assumption made in Sec. IV D that the demon operates at temperature T=Dv, so that the information-acquisition cost is Dv I[vm_0; vr_0]. This is an extra modeling assumption, not a consequence of the dynamics: the heat bath in Eq. (2) has temperature D, and the measurement device is not part of the model. The choice is consequential. If Dv is replaced by D in Eq. (82), the small-error RTP efficiency becomes eta_RTP approximately (tau omega^2 Delta w_engine)/(D ln 2), while eta_AOUP tends to 0 because I_AOUP diverges; for fixed large tau omega^2/D, eta_RTP can exceed 1/(4 ln 2). The paper should either justify T=Dv from a physical model of the measurement process or present Eq. (84) as a convention-dependent expression rather than a universal bound. In particular, the numerical efficiencies in Fig. 7 and the headline bound are not robust to this choice.","section":"Sec. IV D, Eq. (63); Sec. V D, Eqs. (82), (84)"},{"comment":"The closed-loop reduction in Eq. (62) and the engine work extraction in Eq. (80) are computed for the external-work functional W_ext. Section VI shows that the total-work functional W_ext+int leads to an optimal closed-loop work that is independent of the self-propulsion measurement (Eq. (93)), so the measurement advantage is not a property of the total energy cost. The abstract and conclusion should consistently state that the closed-loop benefit and the information engine refer to external work, because the paper's own Sec. VI is presented as a qualification rather than as part of the main claims.","section":"Abstract and Sec. VI"}],"minor_comments":[{"comment":"The notation Dv for the active-noise coefficient is easily misread as the product D times v; please use D_v or another unambiguous symbol.","section":"Sec. II and throughout"},{"comment":"The quantity xvn used for cycles n>0 is defined only in App. C; the main text should state at least briefly that xvn is the expected initial position given the partially relaxed measurement, so the reader is not forced to consult the appendix.","section":"Sec. V B, Eq. (76)"},{"comment":"The comparison in Fig. 7 is presented as eta/Delta w_engine, which removes the model-dependent factor; this normalization is important and should be explained in the main text near the figure reference as well as in the caption.","section":"Sec. V D, Fig. 7"},{"comment":"The derivation of the upper bound uses Delta w_engine <= 1/4 and I_RTP >= ln 2; these two facts are stated nearby but should be assembled explicitly in the text preceding Eq. (84) so the bound is transparent.","section":"Sec. V D, Eq. (84)"}],"recommendation":"major_revision","confidential_remarks":"The paper is competently written and likely publishable after revision. The main issue is the unsubstantiated demon-temperature assumption behind the universal efficiency bound; please ask the authors to either justify the choice T=Dv or soften the claim to a convention-dependent result. The qualitative RTP-over-AOUP ordering may survive, but the quantitative bound and Fig. 7 must be reassessed. The companion-paper overlap should also be checked by the editor."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First the good news: this is a careful, self-contained account of optimal control for active particles in a moving harmonic trap. The open-loop result—optimal protocol identical to the passive particle, with activity only inflating the work variance—is clean, and the variance formulas (Eqs. 34–36) are new. The closed-loop protocol with a single self-propulsion measurement, the explicit work reduction in Eq. (62), and the one-bit information cost for RTPs are all non-obvious and correctly derived. I spot-checked the Euler-Lagrange equations, the τ→0 and τ→∞ limits, and the engine optimization; everything lines up. The paper is also honest about its scope: Section VI shows that if you include internal dissipation in the cost functional, the closed-loop advantage disappears.\n\nThe soft spot is real but localized. The information efficiency η and the bound 1/(4 ln 2) rest on setting the demon temperature to T = Dv (Sec. IV D). That is an extra modeling assumption, not a consequence of the dynamics—the heat bath in Eq. (2) has temperature D, and Dv is an active-noise coefficient with different units. If you instead charge the measurement at the thermal temperature D, the efficiency changes: for RTPs it is proportional to τω^2/D and can exceed the quoted bound; for AOUPs the mutual information diverges as ε→0, sending η_AOUP to zero. So the 'universal' wording in the conclusion is too strong. The paper does flag the assumption, but the abstract and the bound downplay how contingent it is. The engine's qualitative ordering (RTP beats AOUP) likely survives, but the headline number does not.\n\nThat said, the paper is not a one-trick pony. The exact open- and closed-loop protocols, the variance results, and the minimal engine are valuable benchmarks for active-matter stochastic thermodynamics. The derivations are transparent, the simulations match the theory, and the companion-paper structure is fine—this version has all the details.\n\nMy recommendation: send it to peer review. It should be accepted after the authors either (a) rework the efficiency discussion to clearly label 1/(4 ln 2) as conditional on the demon-temperature choice, or (b) justify that choice physically. This is a serious, careful paper with one overstated claim.","headline":"Solid exact results on active-particle control, but the 'universal' information-efficiency bound depends on a demon-temperature assumption the paper states but does not justify.","tokens_in":31858,"tokens_out":3056,"would_cite":true,"duration_ms":28023,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["05.40.-a","05.70.Ln"],"model":"deepseek-v4-flash","headline":"Minimum-work dragging of an active particle is open-loop passive; one measurement per cycle converts activity into extracted work at efficiency up to $1/(4\\ln 2)$.","keywords":["active matter","stochastic thermodynamics","optimal control","information engine","run-and-tumble particle","active Ornstein-Uhlenbeck particle","work extraction","feedback control"],"falsifier":"In a feedback-trap experiment on a run-and-tumble or active Ornstein-Uhlenbeck particle, measure the mean work extracted per engine cycle as a function of measurement error $\\epsilon$: Eqs. (62) and (80) predict a strict $(\\omega^2-\\epsilon^2)$ dependence with zero extraction at $\\epsilon=\\omega$, so observing extraction beyond $\\epsilon=\\omega$ — or a demon whose measurement cost is set by the thermal temperature rather than $D_v$ — would falsify the central claim.","tokens_in":30884,"feed_emoji":"⚡","tokens_out":14100,"duration_ms":120305,"temperature":0.7,"pith_summary":"This paper asks how to drag a single self-propelled particle in a harmonic trap from one position to another in finite time while spending as little external work as possible. The answer depends on whether the controller uses information. With no measurement of the particle's state, the optimal protocol and the average work cost are exactly those of a passive particle, and activity only inflates the fluctuations of the work. With a single initial measurement of the particle's self-propulsion, the optimal protocol changes and the average external work drops below the open-loop value whenever the measurement error is smaller than the amplitude of the self-propulsion. The same machinery motivates a minimal periodic information engine that extracts work from activity, whose information efficiency is bounded by $1/(4\\ln 2)$ and is higher for run-and-tumble particles than for active Ornstein-Uhlenbeck particles.","feed_headline":"One measurement makes active-particle dragging cheaper than open-loop","feed_subtitle":"For error below the swim speed, a feedback trap beats open-loop control and can power a small information engine.","key_machinery":"The argument is carried by a variational cost functional over mean trajectories, $W[\\langle x\\rangle_\\alpha]$, together with the Euler-Lagrange equation $\\langle \\ddot x\\rangle_\\alpha=\\tfrac{1}{2}\\langle \\dot v\\rangle_\\alpha$ that fixes the closed-loop optimum. Activity enters only through the mean self-propulsion $\\langle v(t)\\rangle_\\alpha=v_0e^{-t/\\tau}$, which is identical for run-and-tumble and active Ornstein-Uhlenbeck particles under the matching $D_v/\\tau=\\omega^2$; hence the optimal protocols are model-independent at the level of first moments. The closed-loop benefit is carried by the effective distance $d_{v_0}=\\lambda_f-v_0/(k+1/\\tau)-\\tfrac{\\tau v_0}{2}(1-e^{-t_f/\\tau})$, whose squared term represents the boundary cost, balanced against two extraction terms, and by the nonnegative excess-work identity $\\Delta w\\ge 0$ that becomes Eq. (62) in the presence of measurement noise.","core_discovery":"The central claim is that the elementary task of dragging an active particle in a harmonic trap has exact optimal-control solutions that differ sharply between open- and closed-loop operation. Minimizing the average external work $$\\langle W\\rangle_\\$\\alpha$=\\tfrac{k}{2}[(\\$\\lambda$-\\langle x\\rangle_\\$\\alpha$)^2]$_0^{{t_f}}$+\\$int_0^{{t_f}}$dt\\,(\\langle \\dot x\\rangle_\\$alpha^{2}$-\\langle \\dot x\\rangle_\\$\\alpha$\\langle v\\rangle_\\$\\alpha$)$$ over trap-center protocols with fixed endpoints, the open-loop minimizer is the passive-particle protocol with symmetric jumps, so activity does not change the average cost but increases the work variance. If the controller first measures the initial self-propulsion $v_0$, the optimal protocol acquires linear and exponential pieces with asymmetric jumps, and the measurement-averaged work becomes $\\langle W\\rangle_{ss}-\\tau\\omega^2\\Delta w$ with $\\Delta w\\ge 0$, so the information lowers the external work for finite persistence time and, under Gaussian measurement error $\\epsilon$, remains beneficial for $\\epsilon<\\omega$. Applied periodically with a re-optimized target, the protocol extracts $(\\omega^2-\\epsilon^2)\\tau\\Delta w_{\\rm engine}$ per cycle; dividing by the information-acquisition cost $D_v I$ gives an information efficiency bounded by $1/(4\\ln 2)$, with run-and-tumble particles approaching the bound in the quasistatic, zero-error limit because their discrete self-propulsion costs only one bit of information, whereas the Gaussian AOUP cost diverges as $\\epsilon\\to 0$.","pith_inferences":["The one-bit saturation of the run-and-tumble information cost suggests that any active particle with discrete self-propulsion states will beat Gaussian swimmers in information efficiency at low measurement error, not just the RTP studied here.","The same Euler-Lagrange machinery could be applied to protocols with time-dependent trap stiffness or with more than one measurement per cycle; the paper's closing remarks point toward such machines exceeding the $1/(4\\ln 2)$ bound.","If the measurement cost is set by the ordinary thermal temperature rather than by $D_v$, the numerical efficiencies and the quoted bound change, but the qualitative RTP-over-AOUP ordering is likely to survive because it stems from the one-bit saturation of the RTP mutual information.","Because the mean-work predictions depend only on first moments, any active model with the same conditional mean dynamics should exhibit the same optimal protocols, which is a direct, testable robustness prediction across models."],"forward_implications":["Without feedback, activity buys nothing on average: the cheapest open-loop protocol and its mean work are the passive ones, so the only signature of activity is increased work fluctuations.","With a single self-propulsion measurement, the average external work is reduced whenever the measurement error stays below the self-propulsion amplitude, and the reduction is largest at a finite persistence time; neither passive nor ballistic particles benefit.","The periodic information engine extracts work from self-propulsion for any nonzero measurement outcome, with mean extraction $(\\omega^2-\\epsilon^2)\\tau\\Delta w_{\\rm engine}$ per cycle, and the run-and-tumble version has higher information efficiency than the active Ornstein-Uhlenbeck version.","Because only first moments enter the cost functional, the optimal protocols coincide for RTPs and AOUPs; non-Gaussianity shows up in the work distribution shape and in the information cost rather than in the protocol.","If the cost functional is extended to include the internal dissipation of the active particle, self-propulsion measurements no longer reduce the total work; instead, a finite dragging time minimizes the total cost."],"supporting_citations":[{"why":"Supplies the passive-particle optimal open-loop protocol and the variational calculus method that the paper extends to active particles.","marker":"[2]"},{"why":"Provides the passive limit against which the open-loop active optimization is shown to coincide.","marker":"[41]"},{"why":"Establishes the feedback-work framework for passive particles with an initial measurement that the active self-propulsion measurement generalizes.","marker":"[19]"},{"why":"Gives the active Szilard-engine setting and the information-based work-extraction strategy that the proposed engine is compared with.","marker":"[29]"},{"why":"Provides a dynamic information engine on a single active particle whose force protocol resembles the engine protocol derived here.","marker":"[15]"},{"why":"Fixes the mutual-information accounting used for the thermodynamic cost of measurements and for the information efficiency.","marker":"[21]"},{"why":"Supplies the response-theory context and the finite optimal protocol duration that reappears for the total-work cost functional.","marker":"[10]"},{"why":"Gives the run-and-tumble propagator and steady-state statistics used for the RTP covariances and information cost.","marker":"[37]"}],"fun_headline_variants":["One measurement cuts active-particle dragging cost","Feedback with one measurement beats open-loop for active work","Active particle engine extracts work with single measurement","Run-and-tumble particles hit optimal information efficiency"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The efficiency bound assumes the information-gathering step is priced by the strength of the particle's self-propulsion noise rather than by the ordinary heat-bath temperature, and that the controller pays only external work; if either premise gives way, the quoted work reduction and the $1/(4\\ln 2)$ bound change.","fun_headline_variants_meta":{"raw":{"variants":["One measurement cuts active-particle dragging cost","Feedback with one measurement beats open-loop for active work","Active particle engine extracts work with single measurement","Run-and-tumble particles hit optimal information efficiency"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000978,"raw_usage":{"total_tokens":4231,"prompt_tokens":1098,"completion_tokens":3133,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":714,"completion_tokens_details":{"reasoning_tokens":3076}},"tokens_in":714,"tokens_out":3133,"duration_ms":22225,"temperature":1.0,"reasoning_tokens":3076,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:01:12.741824+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In a feedback-trap experiment on a run-and-tumble or active Ornstein-Uhlenbeck particle, measure the mean work extracted per engine cycle as a function of measurement error $\\epsilon$: Eqs. (62) and (80) predict a strict $(\\omega^2-\\epsilon^2)$ dependence with zero extraction at $\\epsilon=\\omega$, so observing extraction beyond $\\epsilon=\\omega$ — or a demon whose measurement cost is set by the thermal temperature rather than $D_v$ — would falsify the central claim.","supporting_citations":[{"cited_title":"This is illustrated in the bottom panels of Fig","cited_arxiv_id":null,"evidence_quote":"Supplies the passive-particle optimal open-loop protocol and the variational calculus method that the paper extends to active particles."},{"cited_title":"Active Brownian heat engines,","cited_arxiv_id":null,"evidence_quote":"Provides the passive limit against which the open-loop active optimization is shown to coincide."},{"cited_title":"Optimal finite-time pro- cesses in stochastic thermodynamics,","cited_arxiv_id":null,"evidence_quote":"Establishes the feedback-work framework for passive particles with an initial measurement that the active self-propulsion measurement generalizes."},{"cited_title":"Learning pro- tocols for the fast and efficient control of active matter,","cited_arxiv_id":null,"evidence_quote":"Gives the active Szilard-engine setting and the information-based work-extraction strategy that the proposed engine is compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides a dynamic information engine on a single active particle whose force protocol resembles the engine protocol derived here."},{"cited_title":"Optimal control of nonequilibrium systems through au- tomatic differentiation,","cited_arxiv_id":null,"evidence_quote":"Fixes the mutual-information accounting used for the thermodynamic cost of measurements and for the information efficiency."},{"cited_title":"We assumed that the measured value vm 0 given the true value vr 0 is normal distributed around the true value with error ϵ2 P (vm 0 |vr","cited_arxiv_id":null,"evidence_quote":"Supplies the response-theory context and the finite optimal protocol duration that reappears for the total-work cost functional."},{"cited_title":"Maximizing power and velocity of an information engine,","cited_arxiv_id":null,"evidence_quote":"Gives the run-and-tumble propagator and steady-state statistics used for the RTP covariances and information cost."}],"review_version":1}