{"id":"51a1e1a6-ccf1-4548-91f4-528082c538a2","arxiv_id":"2501.02236","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A Wiener-filter method extracts the stochastic active force on a passive probe in an active fluid; it is validated on simulations and applied to E. coli baths.","lead":"The authors use a Wiener filter to separate thermal noise from the force acting on a trapped particle in an active bacterial bath, recovering the fluctuating active force from its trajectory. This could enable direct estimates of entropy production and energy exchange in active and living materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Experimental validation is circular: Appendix B fits α and k/γ to force the residual to be white, so the inferred active force in E. coli baths may be an artifact of the assumed noise model; a passive or killed-bacteria control is needed.","rationale":"The paper proposes a Wiener-filter estimator for the active force acting on a trapped passive probe, with the key assumption that the total force is an additive sum of the active force and a white, Gaussian, delta-correlated thermal noise of variance 2k_BTγ that is uncorrelated with the active force. Under that assumption, the LMMSE solution w* = R⁻¹r with r = ⟨FF⟩ − ⟨ξξ⟩ is mathematically sound, and the numerical demonstrations in Sections III and IV correctly validate the procedure when the assumed model is exactly true. The ABP simulation in Section IV is a useful stress test because the active force is non-Gaussian and the comparison against the known instantaneous force is direct. However, the experimental section lacks any ground truth, and the only diagnostic used is the whitening of the residual thermal force. Because Appendix B optimizes α and k/γ to minimize the deviation of the inferred thermal ACF from the assumed delta function, the whitening is enforced rather than tested. Any colored or correlated component of the true thermal noise, or any mis-specification of the Langevin structure (e.g., viscoelastic memory), will be folded into the inferred active force. This is the most load-bearing weakness because it directly undermines the central claim of 'high statistical accuracy' in the experimental setting, while leaving the method's formal correctness intact. The proposed control experiment—using bacteria-free and killed-bacteria baths—would provide a decisive check: if the method reports substantial active force in the absence of motility, then the experimental claim is not supported; if it reports near-zero force, the concern is substantially allayed. This reasoning aligns with the reader's conditional verdict: the paper is promising but currently lacks the evidence needed to fully support the stated experimental claim. The reader already identified the noise-model assumption as the weakest point, and my analysis agrees that this is the crux; the additional specificity here is the circularity of the Appendix B validation and the concrete control needed to break it. Therefore the verdict remains CONDITIONAL, and I recommend no change to the reader's assessment.","tokens_in":14817,"tokens_out":6519,"duration_ms":68707,"concrete_test":"Perform the identical optical-trapping experiment and analysis pipeline, including the Appendix B parameter scan, on (i) bacteria-free buffer and (ii) the same three concentrations of non-motile (e.g., heat-killed or glutaraldehyde-fixed) E. coli at 37°C. For each control, compute the inferred active force time series, its r.m.s. amplitude, PDF non-Gaussianity, and ACF. If the inferred active force amplitude or non-Gaussian tails in the controls are comparable to those in the live-bacteria measurements, the method cannot distinguish activity from passive medium changes, and the central experimental claim fails. A quantitative threshold: the inferred active-force variance in controls should be below the thermal-noise variance (k_BT/γ) and at least an order of magnitude smaller than the weakest live-bacteria signal (Conc 1).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that the fluctuating active force can be decoded with high statistical accuracy in experiments—rests on the assertion that the thermal noise ξ(t) is white, delta-correlated, and independent of Fact(t). In the experimental section there is no ground truth; the only internal check is Appendix B, where the authors scan α and k/γ to minimize Error = |ACF(inferred random force) − ACF(theory)|/(2k_B T γ), with ACF(theory) being the assumed delta function. This procedure guarantees that the residual after filtering is approximately white by construction. Thus the reported whiteness of the residual and the fitted parameters α≈2.1, k/γ≈190 s⁻¹ do not validate the extraction: any mismatch between the true bath noise and the assumed white form (e.g., colored thermal noise due to bacteria-induced viscoelasticity, or correlations between bacterial collisions and the 'thermal' force) is absorbed into the inferred active force, biasing its PDF, ACF, and the derived De values. The numerical tests in Secs. III–IV cannot resolve this because they generate data from the same additive white-noise model. Therefore the experimental demonstration is not yet evidence for 'high statistical accuracy'; it is evidence only that the parameterization can make the residual look white. A control experiment with a passive bath, or with killed (non-motile) bacteria at identical concentrations, would test whether the method invents active force when none is present.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes a time-domain Wiener-filter (linear minimum mean-square error) estimator for the fluctuating active force Fact(t) acting on a harmonically trapped passive probe in an active bath. The total force F(t) = gamma*xdot(t) + kx(t) is written as Fact(t) plus delta-correlated thermal noise xi(t) of known variance 2kBT*gamma, assumed uncorrelated with Fact(t); the optimal weights w* = R^-1 r are obtained from the measured autocorrelation of F and the thermal-noise autocorrelation, so the filter requires no parametric model of the active force. The method is tested on simulated OU-active-force trajectories with df = De/D0 = 15-200 (reported normalized MSE 0.11-0.35), on simulated trajectories of a probe in a bath of 100 ABPs (qualitative agreement, no error metrics), and on experimental optical-tweezers trajectories of a 5 micron silica particle in motile E. coli baths at three concentrations. The experimental analysis reports non-Gaussian PDFs of the inferred force, double-exponential force ACFs with tau2 in the range 0.34-0.56 s, and active diffusion constants De = 1.97-21.42 um^2/s, all exceeding the thermal value. The paper concludes that active forces can be measured with high statistical accuracy and that the approach is agnostic to the nature of the active force, with implications for estimating entropy production, work, and heat.","tokens_in":15173,"tokens_out":39818,"duration_ms":361627,"significance":"An attractive feature of the paper is that the Wiener filter is constructed from the measured total-force ACF and the assumed thermal-noise ACF only; the derivation in Section II is clean and correct, and the estimator genuinely does not need a parametric model of the active force. The OU simulation is a genuine controlled benchmark (the Appendix B parameter sweep recovers the exact simulation parameters alpha = 2 and k/gamma = 167 s^-1 when the model is correct), and the ABP simulation extends the test to non-Gaussian multi-particle forces. As a result, the numerical core of the paper is sound and reproducible in principle. The experimental data set is also of interest: a concentration series of force-trajectory statistics in a real E. coli bath, with non-Gaussian tails and a two-timescale ACF, has clear value for the active-matter community.","major_comments":[{"comment":"The experimental validation rests on a self-consistency criterion that cannot falsify the assumed noise model. In Appendix B, the parameters alpha and k/gamma are tuned so that the residual force ACF matches the assumed delta-correlated form of amplitude 2kBT*gamma; any mismatch between the true bath noise and the assumed white, uncorrelated thermal component (e.g., bacteria-modified effective viscosity, colored thermal noise from bacterial viscoelasticity, or hydrodynamic coupling between bacterial fluctuations and the probe motion) is absorbed into the inferred active force and biases its PDF, ACF, and the derived De values. The numerical tests in Sections III-IV cannot reveal such a bias because their data are generated from the same additive-white-noise model the filter presupposes. The two-parameter fit is not a pure tautology, since two parameters cannot whiten an arbitrary colored residual, but it is a weakly falsifying test; the fitted value alpha approximately 2.1 is mildly reassuring yet does not constitute external validation. A control experiment in a passive (bacteria-free) or killed non-motile-bacteria bath at matched optical densities is the minimum requirement to support the experimental component of the central claim that the active force is measured with high statistical accuracy.","section":"Section V; Appendix B"},{"comment":"The abstract and conclusion state that the active force is measured with 'high statistical accuracy,' but the normalized MSE values reported in the caption of Fig. 3 are 0.35, 0.26, 0.17, and 0.11 for df = 15, 30, 90, and 200. For the OU model, the ideal infinite-sample LMMSE floor is 1/sqrt(1+df), which is already 0.25 at df = 15, and the experimental De values in Table I correspond to df of about 20, 80, and 214 for the three concentrations. The ratio of active-to-thermal force variance in these experiments is approximately df*dt/(2*tau2), i.e., about 0.15 for Conc 1 and 0.36 for Conc 2, so those measurements lie outside the regime the Introduction itself calls favorable ('when the active force component is comparable or higher compared to the thermal force'). In addition, the realized MSEs exceed the ideal floor by a factor of about 1.4-1.6, which the sampling-time and trajectory-length analysis of Appendix A (reported effects of only 4-6%) does not explain. The accuracy claim should be restricted to the high-df regime, and the sources of the excess error (finite-sample autocorrelation estimation, filter order) should be quantified.","section":"Abstract; Section III, Fig. 3"},{"comment":"The ABP validation is purely qualitative: the text states that the inferred and input active forces 'match reasonably well,' but no error metric is reported for the trajectory comparison, nor for the ACF or PDF comparisons. Since the ABP simulation is the only test of the method against genuinely non-Gaussian, multi-particle active forces and is the main support for the agnosticism claim, a quantitative measure (e.g., normalized MSE or correlation between the simulated and inferred force trajectories, plus a numerical ACF/PDF discrepancy) should be added.","section":"Section IV, Figs. 5-6"},{"comment":"The paper never specifies the discrete-time thermal-noise covariance used to build the <xi xi> vector. For a trajectory sampled at interval dt, the thermal contribution to the discretized force F = gamma*dx/dt + kx has variance 2kBT*gamma/dt, not the continuous-time delta amplitude 2kBT*gamma; Appendix B writes a discretized Langevin equation and then states that the noise variance is alpha*kBT/gamma with alpha theoretically equal to 2, conflating the two conventions (dimensionally alpha*kBT/gamma has units of N^2*s, the continuous-time delta amplitude). The reported simulation results suggest that the implementation itself is consistent, but the paper as written is not reproducible on this point; the discrete covariance (including any 1/dt factor) and its relation to the fitted parameter alpha must be stated explicitly.","section":"Section II (after Eq. (9)); Appendix B"},{"comment":"The text claims that 'both tau1 and tau2 almost remain constant with the bacterial concentrations,' which is contradicted by Table I: tau2 = 0.344 +/- 0.013 s (Conc 1), 0.561 +/- 0.029 s (Conc 2), and 0.463 +/- 0.016 s (Conc 3); the Conc 1-Conc 2 difference is roughly seven combined standard errors. The related statement that tau1 is 'at least one order less than tau2' is also unsupported, since tau2/tau1 is approximately 6.6, 7.1, and 7.8 for Conc 1-3. These claims should be corrected or backed by a significance test.","section":"Section V, Table I"},{"comment":"The reported ACF amplitudes and the derived active diffusion constants (via A2 = gamma^2*De/tau2) carry a bias from the filtering procedure itself. For the Wiener smoother, the estimate spectrum is S_hat_a(omega) = S_a(omega)^2/(S_a(omega)+S_xi(omega)), so the inferred ACF underestimates the true ACF by the factor S_a/(S_a+S_xi); near the characteristic frequency this factor is approximately 0.91 for Conc 1 (df about 20) and approaches unity only at the highest concentration. The ACFs and the De values in Table I should either be corrected by the known filter transfer function of Eq. (8) or the residual bias should be quantified.","section":"Section V, Table I"}],"minor_comments":[{"comment":"The implementation is underspecified: please state the filter length, whether the filter is causal or a non-causal smoother, how the autocorrelation matrix R is estimated and inverted for trajectories with tens of thousands of points, and whether the filtering is done in the time or frequency domain.","section":"Section II"},{"comment":"The probe dynamics in Eq. (D3) are two-dimensional; please state explicitly whether the x and y components are filtered separately and whether the reported results correspond to a single Cartesian component.","section":"Section IV"},{"comment":"The caption lists the panel groups out of sequence ((h)-(j), (k), (l)-(n), (o), (p)-(s)), which makes the inferred active-force PDFs hard to locate; please reorder or renumber the panels.","section":"Fig. 7"},{"comment":"'Agnostic to the nature of the active force' should be qualified, since the method is agnostic to the parametric form of the active force but assumes the thermal force is white, has known variance, and is uncorrelated with the active force.","section":"Abstract and conclusion"},{"comment":"Refs. [29,30] are cited in support of the 'wall curvature dependency' of the average active force between passive particles, but both papers address swim pressure on walls; please verify or replace these citations.","section":"Introduction"},{"comment":"Please state how many independent trajectories are used to compute the main-text MSE values in Fig. 3; Appendix A mentions averaging over multiple independent inputs, but the reported numbers do not include this information.","section":"Section III"},{"comment":"The scalar error Error = |ACF(Inferred random force) - ACF(theory)|/(2kBT*gamma) is shown in the insets of Fig. 10 without specifying the lag range over which the absolute difference is accumulated; please define it.","section":"Appendix B"},{"comment":"The fitted parameters f, sigma_g, and sigma_e of the weighted Gaussian-plus-exponential PDFs in Figs. 7(k) and 7(o) are not reported numerically; reporting them would enable quantitative comparison with the enhanced-diffusion results of Ref. [7] and with earlier active-bath force measurements (Refs. [27,61]).","section":"Section V"},{"comment":"The manuscript contains no data and code availability statement; given that the filter implementation details are not fully specified in the text, sharing the analysis code would substantially improve reproducibility.","section":"Manuscript"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the decisive issue is the experimental validation. The numerical LMMSE derivation and the OU benchmark are sound; the main risk is that the fitted-force statistics in the E. coli experiments could be an artifact of the assumed white-noise model, so I would regard a passive or killed-bacteria control as the gating requirement for acceptance. I also recommend asking the authors to position the contribution explicitly against Refs. [27] and [61], which have already measured force statistics for trapped probes in active baths; the stated novelty (full time-series extraction via a Wiener filter) is discernible but should be argued explicitly. The remaining issues (accuracy-claim calibration, discrete-time conventions, internal inconsistencies in Table I) are fixable by revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the paper. The headline: the numerical core is a legitimate, useful contribution—applying a classical Wiener filter to extract the full trajectory of fluctuating active force on a trapped probe, with validation against simulated OU and ABP baths where the input force is known. The ABP test is the strongest part: it shows non-Gaussian force PDFs and multi-timescale correlations can be recovered, which is genuinely new and worth knowing. The LMMSE derivation is correct, the writing is clear, and the parameter-sweep analysis in Appendix B for the numerical case is a real check. So I don't share the reader's skepticism about the method itself. The soft spot is exactly where the stress-test lands: the experimental section. In the E. coli baths, there is no independent ground truth for the active force. The only check is the Appendix B calibration, where alpha and k/gamma are selected to make the inferred thermal-force ACF match the assumed delta function. That procedure guarantees the residual looks white; it cannot validate the decomposition. The reported whiteness is a consequence of the fit, not evidence for it. A passive-bath or killed-bacteria control at matched concentrations would test whether the method invents active force when none is present. Without such a control, the claim of 'high statistical accuracy' in experiments is unsupported. Also, the OU simulations show normalized MSE between 0.11 and 0.35, which is moderate, not 'high accuracy' at low activity; the phrasing should be more careful. A further issue: the filter assumes constant gamma and k, but bacteria can alter the local viscosity and effective trap dynamics. If that happens, the net force from Eq. (3) is biased, and the filter subtracts the wrong noise spectrum, pushing that error into the inferred active force and the De values in Table I. Who benefits: experimentalists using optical tweezers in active baths, and theorists needing trajectory-level active-force estimates for stochastic thermodynamics. The paper deserves peer review—the numerical result is solid and the experimental flaw is fixable with a control experiment. I'd send it out with a request for major revision focused on validation, not novelty. I would cite the numerical part in my own work on active-force inference.","headline":"A useful numerical demonstration of Wiener-filter-based active-force extraction, but the experimental validation is undercut by a circular noise-calibration step.","tokens_in":15705,"tokens_out":2258,"would_cite":true,"duration_ms":23687,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A Wiener filter recovers the full fluctuating active force on a trapped particle in an active bath by subtracting the thermal noise, with tests in simulations and E. coli suspensions.","keywords":["active matter","Wiener filter","active force fluctuations","optical tweezers","bacterial active bath","non-Gaussian statistics","stochastic thermodynamics"],"falsifier":"Place a trapped bead in the identical buffer with no bacteria and run the full filter; any nonzero inferred active-force signal, or any deviation of the inferred thermal autocorrelation from a delta function of strength $2 k_B T \\gamma$, would falsify the assumption that the subtraction is clean.","tokens_in":14639,"feed_emoji":"🦠","tokens_out":6329,"duration_ms":56489,"temperature":0.7,"pith_summary":"The paper claims that the stochastic active force acting on a harmonically trapped passive particle in an active fluid can be measured as a full time series, not just as a time-averaged quantity. Since the recorded force is the sum of a rapidly fluctuating thermal force and the slower active force, the authors use a time-domain Wiener filter to remove the known white thermal component and estimate the active force trajectory with minimum mean-square error. They validate the approach in two numerical settings, an Ornstein-Uhlenbeck active force and a bath of active Brownian particles, and then apply it to optical-tweezers trajectories of a silica bead in suspensions of motile E. coli at three concentrations. The inferred active forces are non-Gaussian and their autocorrelations are double-exponential with a slow timescale comparable to bacterial persistence, suggesting the method can expose the true statistical nature of active forces.","feed_headline":"Active force on a trapped probe decoded from its jiggle","feed_subtitle":"Filtering thermal noise from trajectories yields bacterial force statistics and a route to entropy production.","key_machinery":"The central object is the time-domain Wiener filter, a linear minimum mean-square error estimator of the form $\\hat{F}_{\\mathrm{act}} = w^{*T} F$ with $w^* = R^{-1} r$. Its key simplification is Eq. (9): $r = \\langle F F \\rangle - \\langle \\xi \\xi \\rangle$, which replaces the unknown cross-correlation between active and thermal forces by the known thermal autocorrelation (nonzero only at zero lag, equal to $2 k_B T \\gamma$). The paper also introduces an iterative refinement of the two unknown scalar parameters $\\alpha$ (thermal noise strength scaling) and $k/\\gamma$ (inverse relaxation time), fixing them by requiring the inferred thermal noise to have the expected white spectrum, which makes the method usable when bacteria modify the local viscosity.","core_discovery":"Given a Langevin description $\\gamma \\dot{x} + kx = F(t) = \\xi(t) + F_{\\mathrm{act}}(t)$ with known trap stiffness $k$, friction $\\gamma$, and white thermal noise of variance $2 k_B T \\gamma$, the total force $F$ is computable from the trajectory. Because the thermal noise is uncorrelated with the active force, the optimal Wiener weight vector reduces to $w^* = R^{-1} r$ where $r = \\langle F F \\rangle - \\langle \\xi \\xi \\rangle$; hence the estimate $\\hat{F}_{\\mathrm{act}} = w^{*T} F$ depends only on measurable statistics of the trajectory and the known thermal spectrum. The authors show that this filtered trajectory reproduces the input active force's autocorrelation and probability distribution in both numerical scenarios, and that in the E. coli experiment the recovered force displays non-Gaussian tails and a two-timescale correlation decay, with active diffusion coefficients $D_e = 1.97$, $8$, and $21.42\\ \\mu\\mathrm{m}^2/\\mathrm{s}$ for increasing bacterial concentration.","pith_inferences":["A decisive control experiment would run the same protocol on a bead in buffer without bacteria; a nonzero inferred active force would directly measure the noise-leakage floor of the filter.","The method's resolution is limited by the ratio of active to thermal force strength; at low bacterial concentrations the error normalized by variance grows (about 0.35 at $d_f=15$ in simulations), so the practical detectability floor for active forces in weak baths deserves explicit characterization.","Because the two-timescale autocorrelation is extracted from the same trajectories, the method could be used to map spatial heterogeneity of active forces by scanning the trap position across a bacterial suspension, yielding a force 'image' of the active bath.","The assumption of a fixed, known temperature may fail in strongly active baths where swimmers dissipate heat locally; combining the filter with simultaneous temperature measurement could disentangle genuine active force from a thermal renormalization."],"forward_implications":["With the full active-force trajectory in hand, stochastic-thermodynamics quantities such as heat, work, and entropy production can be estimated directly from experimental records instead of relying on lower-bound inference methods.","Because the filter is agnostic to the nature of the active force, the same protocol transfers to other active baths — active Brownian particles, swimming microorganisms, or engineered active colloids — without re-deriving a force model.","The experimental recovery of non-Gaussian, double-exponential active forces provides a direct test for theoretical models: force statistics inferred this way can be compared with predictions from Poisson-shot-noise or other non-Gaussian active-force models.","The method extends to multiple passive particles and, with modifications, to viscoelastic fluids, opening a route to force measurements in living, inherently viscoelastic tissues."],"supporting_citations":[{"why":"Supplies the Wiener filter and linear minimum mean-square error estimation machinery that is the core of the method.","marker":"[46]"},{"why":"Provides the exponentially correlated Ornstein-Uhlenbeck model for the active force and the bacterial persistence timescale used as a numerical benchmark.","marker":"[10]"},{"why":"Supplies the double-exponential autocorrelation fitting form and the interpretation of its two relaxation timescales.","marker":"[27]"},{"why":"Provides the particle tracking algorithm used to convert experimental camera images into position trajectories.","marker":"[53]"},{"why":"Provides the OU active-force model and the framework connecting force trajectories to entropy production in active matter.","marker":"[36]"},{"why":"Documents the non-Gaussian enhanced diffusion in active baths that motivates the need to measure active force statistics directly.","marker":"[7]"}],"fun_headline_variants":["Filtering noise exposes active forces in bacterial baths","Wiener filter decodes active force from crowded trajectories","Trajectory analysis uncovers bacterial force fluctuations","Active forces in E. coli baths read from particle paths","Noise-removal technique reveals stochastic forces in active matter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The thermal force is exactly white noise with known variance $2 k_B T \\gamma$ and is completely uncorrelated with the active force; if active swimmers change the effective viscosity or add memory, the filter subtracts the wrong noise spectrum.","fun_headline_variants_meta":{"raw":{"variants":["Filtering noise exposes active forces in bacterial baths","Wiener filter decodes active force from crowded trajectories","Trajectory analysis uncovers bacterial force fluctuations","Active forces in E. coli baths read from particle paths","Noise-removal technique reveals stochastic forces in active matter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000887,"raw_usage":{"total_tokens":3823,"prompt_tokens":934,"completion_tokens":2889,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":2812}},"tokens_in":550,"tokens_out":2889,"duration_ms":17540,"temperature":1.0,"reasoning_tokens":2812,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:14:25.669553+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Place a trapped bead in the identical buffer with no bacteria and run the full filter; any nonzero inferred active-force signal, or any deviation of the inferred thermal autocorrelation from a delta function of strength $2 k_B T \\gamma$, would falsify the assumption that the subtraction is clean.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Wiener filter and linear minimum mean-square error estimation machinery that is the core of the method."},{"cited_title":"Wiener, Differential-space, Journal of Mathematics and Physics 2, 131 (1923)","cited_arxiv_id":null,"evidence_quote":"Provides the particle tracking algorithm used to convert experimental camera images into position trajectories."},{"cited_title":"Smallenburg and H","cited_arxiv_id":null,"evidence_quote":"Provides the OU active-force model and the framework connecting force trajectories to entropy production in active matter."},{"cited_title":"Fodor, C","cited_arxiv_id":null,"evidence_quote":"Documents the non-Gaussian enhanced diffusion in active baths that motivates the need to measure active force statistics directly."}],"review_version":1}