Pith. sign in

REVIEW 6 major objections 9 minor 67 references

Decoding active force fluctuations from spatial trajectories of active systems

T0 review · 6 major / 9 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read 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.

desk verdict A useful numerical demonstration of Wiener-filter-based active-force extraction, but the experimental validation is undercut by a circular noise-calibration step. read the letter →

arxiv 2501.02236 v2 pith:LF2JE7SH submitted 2025-01-04 cond-mat.soft cond-mat.stat-mech

Anisha Majhi , Biswajit Das , Subhadeep Gupta , Anand Dev Ranjan , Amirul Islam Mallick , Shuvojit Paul , Ayan Banerjee This is my paper · ORCID
classification cond-mat.softcond-mat.stat-mech
keywords activematterWienerfilterforcefluctuationsopticaltweezersbacterialbathnon-Gaussianstatisticsstochasticthermodynamics
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

6 major / 9 minor

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.

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 (6)
  1. [Section V; Appendix B] 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.
  2. [Abstract; Section III, Fig. 3] 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.
  3. [Section IV, Figs. 5-6] 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.
  4. [Section II (after Eq. (9)); Appendix B] 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.
  5. [Section V, Table I] 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.
  6. [Section V, Table I] 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.
minor comments (9)
  1. [Section II] 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.
  2. [Section IV] 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.
  3. [Fig. 7] 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.
  4. [Abstract and conclusion] '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.
  5. [Introduction] 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.
  6. [Section III] 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.
  7. [Appendix B] 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.
  8. [Section V] 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]).
  9. [Manuscript] 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.

Circularity Check

1 steps flagged · score 3.0 of 10

Experimental validation is partially circular: Appendix B fits alpha and k/gamma to minimize the residual-noise ACF error, so the observed whiteness of the inferred thermal force is enforced by construction; numerical benchmarks remain non-circular.

  1. fitted input called prediction [Appendix B; applied in Section V (E. coli experiment), Figs. 7 and 10]
    "Therefore, we write the variance of the noise as αkBT /γ (where theoretically α should be equal to 2 ), and iteratively vary the inverse timescale k/γ and α to obtain the noise with properties the same as known previously. ... The corresponding Errors for each parameter sweep are plotted as the insets of Fig. 10(a)-(d), and it is defined as, Error = |ACF(Inferred random force) - ACF(theory)|/(2kBT γ)."

    For the experimental E. coli baths there is no ground-truth active force. The only internal check is that the inferred thermal residual has the assumed white ACF, but alpha and k/gamma are selected by minimizing exactly that deviation (Error = |ACF(inferred random force) - ACF(theory)|/(2 k_B T gamma)). Thus a white residual is produced by construction, not independently verified. The Wiener filter that yields the active force uses the same assumed white-noise variance and independence (Eq. 9), so any colored or correlated thermal component in the real bacteria bath is absorbed into the inferred active force, biasing its PDF, ACF, and the De values obtained from the double-exponential fit. The numerical tests in Secs.

full rationale

The core Wiener-filter derivation in Sec. II is not circular: it is a standard LMMSE estimator, and in the numerical scenarios the inferred active force is compared with a known input force, providing an external benchmark. The conclusion that the method is 'agnostic to the nature of the active force' is supported by the two different simulated active-force models. The circularity burden is confined to the experimental demonstration: because alpha and k/gamma are optimized to force the inferred thermal-noise ACF to match the assumed white form, the whiteness check validates the assumption only in a tautological sense. A passive or killed-bacteria control would be needed to exclude the possibility that the method manufactures active force from model mismatch. No load-bearing self-citation chain was found; the paper's own prior work is cited for background and related methods, not as the basis for the filter. Overall, the paper has substantial independent content, so the score is moderate rather than severe.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method rests on standard LMMSE estimation, but its experimental deployment requires fitting alpha and k/gamma, and the extracted De values are fit products. In the numerical validations the same assumptions are controlled, which is the main source of independent support.

free parameters (5)
  • alpha (thermal noise strength multiplier) = 2.1 for Conc 3 (experiment); 2 for numerics
    In Appendix B, alpha is iteratively varied to minimize the difference between the inferred thermal-force ACF and the assumed white-noise form; this calibrates the noise variance used in the Wiener filter.
  • k/gamma (inverse system timescale) = 190 s^-1 for Conc 3; 167 s^-1 for numerics
    Same iterative calibration in Appendix B; the value is fitted to make the residual thermal noise appear white, not independently measured for the bacterial baths.
  • A1, tau1, A2, tau2 (double-exponential ACF fit parameters) = A1 4.3e-3 to 35.3e-3 pN^2, tau1 0.052-0.079 s, A2 10.1e-3 to 81.4e-3 pN^2, tau2 0.344-0.561 s across concentrations
    Table I fits these four parameters to the ACF of the inferred active force in the bacterial bath; they are not predictions and are used to compute De.
  • De (active diffusion constant) per concentration = 1.97, 8.0, 21.42 um^2/s for Conc 1, 2, 3
    Computed from A2 via A2 = gamma^2 De / tau2, so these numbers are derived from fit parameters rather than independent measurements.
  • PDF fit parameters f, sigma_g, sigma_e for weighted Gaussian+exponential distribution = not reported numerically
    Used to fit the experimental position and force PDFs in Fig. 7(k),(o); values are fitted to the data.
assumptions (5)
  • domain assumption The probe obeys the overdamped Langevin equation (Eq. 1) with constant friction gamma and harmonic trap stiffness k.
    This is the starting model for both simulations and experiments; if memory or position-dependent drag is present, the total force estimated by Eq. (3) is wrong.
  • domain assumption The thermal force xi is delta-correlated with zero mean and variance 2kBT gamma, and is uncorrelated with the active force Fact.
    Used in Eq. (9) to replace the cross-correlation r with <F F> - <xi xi>; if the noise is colored or correlated with Fact, the Wiener filter becomes biased.
  • domain assumption The force fluctuations are stationary.
    Stated at the start of Sec. II ('Assuming the process to be stationary'); required for the time-averaged correlations R and r to be meaningful.
  • standard math Wiener filter optimality: the LMMSE solution w* = R^{-1} r is the appropriate estimator for Fact given F.
    Standard signal-processing result; it gives the optimal linear estimate under the second-order statistics, but not the globally optimal estimator for non-Gaussian Fact.
  • domain assumption In the bacterial bath, the only effect of activity on the solvent is through Fact; the medium remains Newtonian with the same gamma used in the fit.
    Appendix B implicitly assumes that after fitting alpha and k/gamma the Langevin structure still holds; bacterial flagella could alter the local hydrodynamics beyond this.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Decoding active force fluctuations from spatial trajectories of active systems." pith.science (2026). https://pith.science/paper/LF2JE7SH

@misc{pith2026250102236,
  author       = {Pith},
  title        = {Pith review of: Decoding active force fluctuations from spatial trajectories of active systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LF2JE7SH}},
  note         = {Machine review of arXiv:2501.02236}
}
read the original abstract

Mesoscopic active systems exhibit various unique behaviours - absent in passive systems - due to the forces generated by the corresponding constituents by converting their available free energies. However, estimating these forces - which are also stochastic and remain intertwined with the thermal noise - is especially non-trivial. Here, we introduce a technique to extract such fluctuating active forces acting on a passive particle immersed in an active bath with high statistical accuracy by filtering out the related thermal noise. We first test the efficacy of our method under numerical scenarios with different types of activity, and then apply it to the experimental trajectories of a microscopic particle (optically) trapped inside an active bath consisting of motile \textit{E.Coli.} bacteria. We believe that our simple yet powerful approach, which appears agnostic to the nature of the active force, should enable accurate measurement of force dynamics in living matter and potentially allow direct but reliable estimation of key thermodynamic parameters such as heat, work, and entropy production.

Figures

Figures reproduced from arXiv: 2501.02236 by the authors.

Figure 1
Figure 1. FIG. 1. Numerically generated position fluctuations of an [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Magnified force trajectories from the numerical scenario I for different [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a)-(c) are the positional probability density functions corresponding to the numerical trajectories of a passive probe in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The trajectories of the constituent forces acting on a passive probe immersed in a bath of ABPs are simulated. To [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Statistical properties of the numerically generated active forces (line) are plotted against their inferred estimates [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Schematic of an optically confined passive probe in motile [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Mean square error (MSE) plotted for various sam [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Panels (a)–(f) display results for [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a)-(b) Experimental (for the highest active [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 56 canonical work pages

  1. [1]

    Passive Particle: The passive particle, located at rp, experiences forces due to interactions with ABPs and a harmonic trapping force

    Governing Equations Active Particles: The position ri = (xi, yi) and orien- tation θi of the i-th ABP evolve as dri = v0e(θi) + 1 γactive Fint i dt + p 2Dactive dWi(t), (D1) dθi = p 2Drot dW θ i (t), (D2) where, v0 is the self-propulsion speed, e(θi) = (cos θi, sin θi) is the unit vector in the direction of motion, γactive = 6 πηr active is the friction c...

    work page

  2. [2]

    Inter-particle forces were computed as follows:

    Simulation Details The SDEs were discretized using the Euler–Maruyama method with timestep ∆ t = 0 .0005 s over a simulation duration of 200 s. Inter-particle forces were computed as follows:

    work page

  3. [3]

    These forces were symmetrically distributed between particle pairs to satisfy Newton’s third law

    Active-Active Interactions: Steric repulsion was modeled for pairs of ABPs overlapping within a distance of 2ractive using a force proportional to the overlap. These forces were symmetrically distributed between particle pairs to satisfy Newton’s third law

    work page

  4. [4]

    The resulting forces are applied oppositely to the ABPs and the passive par- ticle

    Active-Passive Interactions: A similar steric repul- sion was employed for ABP and passive particle pairs within a distance of ractive + rpassive. The resulting forces are applied oppositely to the ABPs and the passive par- ticle

    work page

  5. [5]

    Trap Force: The passive particle is confined by a harmonic potential centred at ( L/2, L/2). Positions and orientations are updated in each time step by combining the deterministic contributions from forces with stochastic contributions from Gaussian noise, which are scaled according to the relevant diffusion coef- ficients. 12

    work page

  6. [6]

    Data Collection and Analysis Throughout the simulation, trajectories, forces, and an array of observables were meticulously recorded to facilitate thorough post-processing and analysis, thereby elucidating the efficacy of the filter as detailed in this study. ACKNOWLEDGMENTS The work is supported by IISER Kolkata, and the Sci- ence and Engineering Researc...

    work page 2022

  7. [7]

    Fodor, C

    E. Fodor, C. Nardini, M. E. Cates, J. Tailleur, P. Visco, and F. van Wijland, How far from equilibrium is active matter?, Physical Review Letters 117, 038103 (2016)

    work page 2016

  8. [8]

    Ramaswamy, Active matter, Journal of Statistical Me- chanics: Theory and Experiment 2017, 054002 (2017)

    S. Ramaswamy, Active matter, Journal of Statistical Me- chanics: Theory and Experiment 2017, 054002 (2017)

    2017

Show all 67 references
  1. [9]

    M. t. Vrugt and R. Wittkowski, A review of active matter reviews, arXiv preprint arXiv:2405.15751 (2024)

    2024 arXiv

  2. [10]

    Bechinger, R

    C. Bechinger, R. Di Leonardo, H. L¨ owen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Reviews of Modern Physics 88, 045006 (2016)

    2016

  3. [11]

    M. J. Bowick, N. Fakhri, M. C. Marchetti, and S. Ra- maswamy, Symmetry, thermodynamics, and topology in active matter, Physical Review X 12, 010501 (2022)

    2022

  4. [12]

    Wu and A

    X.-L. Wu and A. Libchaber, Particle diffusion in a quasi- two-dimensional bacterial bath, Physical Review Letters 84, 3017 (2000)

    2000

  5. [13]

    K. C. Leptos, J. S. Guasto, J. P. Gollub, A. I. Pesci, and R. E. Goldstein, Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms, Physical Review Letters 103, 198103 (2009)

    2009

  6. [14]

    Argun, A.-R

    A. Argun, A.-R. Moradi, E. Pin¸ ce, G. B. Bagci, A. Im- parato, and G. Volpe, Non-boltzmann stationary dis- tributions and nonequilibrium relations in active baths, Physical Review E 94, 062150 (2016)

    2016

  7. [15]

    Ortlieb, S

    L. Ortlieb, S. Rafa ¨ ı, P. Peyla, C. Wagner, and T. John, Statistics of colloidal suspensions stirred by microswim- mers, Physical Review Letters 122, 148101 (2019)

    2019

  8. [16]

    Maggi, M

    C. Maggi, M. Paoluzzi, N. Pellicciotta, A. Lepore, L. An- gelani, and R. Di Leonardo, Generalized energy equipar- tition in harmonic oscillators driven by active baths, Physical Review Letters 113, 238303 (2014)

    2014

  9. [17]

    Y. B. Dor, Y. Kafri, M. Kardar, and J. Tailleur, Passive objects in confined active fluids: A localization transi- tion, Phys. Rev. E 106, 044604 (2022)

    2022

  10. [18]

    Reichert and T

    J. Reichert and T. Voigtmann, Tracer dynamics in crowded active-particle suspensions, Soft Matter 17, 10492 (2021)

    2021

  11. [19]

    Kushwaha, V

    P. Kushwaha, V. Semwal, S. Maity, S. Mishra, and V. Chikkadi, Phase separation of passive particles in ac- tive liquids, Physical Review E 108, 034603 (2023)

    2023

  12. [20]

    Singh and A

    C. Singh and A. Chaudhuri, Anomalous dynamics of a passive droplet in active turbulence, Nature Communi- cations 15, 3704 (2024)

    2024

  13. [21]

    Caprini, A

    L. Caprini, A. Ldov, R. K. Gupta, H. Ellenberg, R. Wittmann, H. L¨ owen, and C. Scholz, Emergent mem- ory from tapping collisions in active granular matter, Communications Physics 7, 52 (2024)

    2024

  14. [22]

    Lagarde, N

    A. Lagarde, N. Dag` es, T. Nemoto, V. D´ emery, D. Bar- tolo, and T. Gibaud, Colloidal transport in bacteria sus- pensions: from bacteria collision to anomalous and en- hanced diffusion, Soft Matter 16, 7503 (2020)

    2020

  15. [23]

    Nordanger, A

    H. Nordanger, A. Morozov, and J. Stenhammar, Anisotropic diffusion of ellipsoidal tracers in microswim- mer suspensions, Phys. Rev. Fluids 7, 013103 (2022)

    2022

  16. [24]

    Santra, Dynamical fluctuations of a tracer coupled to active and passive particles, Journal of Physics: Com- plexity 4, 015013 (2023)

    I. Santra, Dynamical fluctuations of a tracer coupled to active and passive particles, Journal of Physics: Com- plexity 4, 015013 (2023)

    2023

  17. [25]

    Goswami, A

    K. Goswami, A. G. Cherstvy, A. Godec, and R. Met- zler, Anomalous diffusion of active brownian particles in responsive elastic gels: Nonergodicity, non-gaussianity, and distributions of trapping times, Phys. Rev. E 110, 044609 (2024)

    2024

  18. [26]

    Di Leonardo, L

    R. Di Leonardo, L. Angelani, D. Dell’Arciprete, G. Ruocco, V. Iebba, S. Schippa, M. P. Conte, F. Mecarini, F. De Angelis, and E. Di Fabrizio, Bacterial ratchet motors, Proceedings of the National Academy of Sciences 107, 9541 (2010)

    2010

  19. [27]

    Sokolov, M

    A. Sokolov, M. M. Apodaca, B. A. Grzybowski, and I. S. Aranson, Swimming bacteria power microscopic gears, Proceedings of the National Academy of Sciences 107, 969 (2010)

    2010

  20. [28]

    Zaeifi Yamchi and A

    M. Zaeifi Yamchi and A. Naji, Effective interactions be- tween inclusions in an active bath, The Journal of chem- ical physics 147 (2017)

    2017

  21. [29]

    Y. Baek, A. P. Solon, X. Xu, N. Nikola, and Y. Kafri, Generic long-range interactions between passive bodies in an active fluid, Phys. Rev. Lett. 120, 058002 (2018)

    2018

  22. [30]

    J. P. Hernandez-Ortiz, C. G. Stoltz, and M. D. Graham, Transport and collective dynamics in suspensions of con- fined swimming particles, Phys. Rev. Lett. 95, 204501 (2005)

    2005

  23. [31]

    Angelani, C

    L. Angelani, C. Maggi, M. L. Bernardini, A. Rizzo, and R. Di Leonardo, Effective interactions between colloidal particles suspended in a bath of swimming cells, Phys. Rev. Lett. 107, 138302 (2011)

    2011

  24. [32]

    S. Paul, A. Jayaram, N. Narinder, T. Speck, and C. Bechinger, Force generation in confined active fluids: The role of microstructure, Physical Review Letters 129, 13 058001 (2022)

    2022

  25. [33]

    Jayaram and T

    A. Jayaram and T. Speck, Effective dynamics and fluc- tuations of a trapped probe moving in a fluid of active hard discs (a), Europhysics Letters 143, 17005 (2023)

    2023

  26. [34]

    J. Shea, G. Jung, and F. Schmid, Force renormalization for probes immersed in an active bath, Soft Matter 20, 1767 (2024)

    2024

  27. [35]

    A. P. Solon, Y. Fily, A. Baskaran, M. E. Cates, Y. Kafri, M. Kardar, and J. Tailleur, Pressure is not a state func- tion for generic active fluids, Nature physics 11, 673 (2015)

    2015

  28. [36]

    Smallenburg and H

    F. Smallenburg and H. L¨ owen, Swim pressure on walls with curves and corners, Phys. Rev. E 92, 032304 (2015)

    2015

  29. [37]

    D. Ray, C. Reichhardt, and C. J. O. Reichhardt, Casimir effect in active matter systems, Phys. Rev. E 90, 013019 (2014)

    2014

  30. [38]

    R. Ni, M. A. Cohen Stuart, and P. G. Bolhuis, Tun- able long range forces mediated by self-propelled colloidal hard spheres, Phys. Rev. Lett. 114, 018302 (2015)

    2015

  31. [39]

    P. Liu, S. Ye, F. Ye, K. Chen, and M. Yang, Constraint dependence of active depletion forces on passive particles, Phys. Rev. Lett. 124, 158001 (2020)

    2020

  32. [40]

    Di Bello, R

    C. Di Bello, R. Majumdar, R. Marathe, R. Metzler, and ´E. Rold´ an, Brownian particle in a poisson-shot-noise ac- tive bath: Exact statistics, effective temperature, and inference, Annalen der Physik , 2300427 (2024)

    2024

  33. [41]

    Rold´ an, J

    ´E. Rold´ an, J. Barral, P. Martin, J. M. Parrondo, and F. J¨ ulicher, Quantifying entropy production in active fluctuations of the hair-cell bundle from time irreversibil- ity and uncertainty relations, New Journal of Physics 23, 083013 (2021)

    2021

  34. [42]

    Dabelow, S

    L. Dabelow, S. Bo, and R. Eichhorn, Irreversibility in active matter systems: Fluctuation theorem and mutual information, Physical Review X 9, 021009 (2019)

    2019

  35. [43]

    S. K. Manikandan, S. Ghosh, A. Kundu, B. Das, V. Agrawal, D. Mitra, A. Banerjee, and S. Krishna- murthy, Quantitative analysis of non-equilibrium sys- tems from short-time experimental data, Communica- tions Physics 4, 258 (2021)

    2021

  36. [44]

    B. Das, S. K. Manikandan, S. Paul, A. Kundu, S. Kr- ishnamurthy, and A. Banerjee, Tuning irreversibility of mesoscopic processes using hydrodynamic interactions, arXiv preprint arXiv:2405.00800 (2024)

    2024 arXiv

  37. [45]

    Sekimoto, Langevin equation and thermodynamics, Progress of Theoretical Physics Supplement 130, 17 (1998)

    K. Sekimoto, Langevin equation and thermodynamics, Progress of Theoretical Physics Supplement 130, 17 (1998)

    1998

  38. [46]

    B. Das, S. Paul, S. K. Manikandan, and A. Banerjee, En- hanced directionality of active processes in a viscoelastic bath, New Journal of Physics 25, 093051 (2023)

    2023

  39. [47]

    Ghosh, A

    T. Ghosh, A. Majhi, A. Kundu, A. Banerjee, and B. Sinha, Actin contractility and endocytosis cre- ate apico-basal tension gradient in hela cells, bioRxiv 10.1101/2025.02.17.638627 (2025)

    2025 doi

  40. [48]

    J. Chen, D. Yan, and Y. Chen, Understanding the driv- ing force for cell migration plasticity, Biophysical Journal 122, 3570 (2023)

    2023

  41. [49]

    Saraswathibhatla, E

    A. Saraswathibhatla, E. E. Galles, and J. Notbohm, Spa- tiotemporal force and motion in collective cell migration, Scientific Data 7, 197 (2020)

    2020

  42. [50]

    Sabass, M

    B. Sabass, M. D. Koch, G. Liu, H. A. Stone, and J. W. Shaevitz, Force generation by groups of migrating bac- teria, Proceedings of the National Academy of Sciences 114, 7266 (2017)

    2017

  43. [51]

    Heisenberg and Y

    C.-P. Heisenberg and Y. Bella ¨ ıche, Forces in tissue mor- phogenesis and patterning, Cell 153, 948 (2013)

    2013

  44. [52]

    Wiener, Extrapolation, interpolation, and smoothing of stationary time series: with engineering applications (The MIT press, 1949)

    N. Wiener, Extrapolation, interpolation, and smoothing of stationary time series: with engineering applications (The MIT press, 1949)

    1949

  45. [53]

    Wiener, Differential-space, Journal of Mathematics and Physics 2, 131 (1923)

    N. Wiener, Differential-space, Journal of Mathematics and Physics 2, 131 (1923)

    1923

  46. [54]

    Boulfelfel, R

    D. Boulfelfel, R. Rangayyan, L. Hahn, and R. Kloiber, Three-dimensional restoration of single photon emission computed tomography images, IEEE transactions on nu- clear science 41, 1746 (1994)

    1994

  47. [55]

    P. S. Diniz, Adaptive filtering , Vol. 5 (Springer, 2020)

    2020

  48. [56]

    Fricks, L

    J. Fricks, L. Yao, T. C. Elston, and M. G. Forest, Time- domain methods for diffusive transport in soft matter, SIAM journal on applied mathematics 69, 1277 (2009)

    2009

  49. [57]

    S. Paul, N. Narinder, A. Banerjee, K. R. Nayak, J. Steindl, and C. Bechinger, Bayesian inference of the viscoelastic properties of a jeffrey’s fluid using optical tweezers, Scientific Reports 11, 2023 (2021)

    2021

  50. [58]

    com/help/econ/varm.html

    MathWorks, Var model (varm), https://in.mathworks. com/help/econ/varm.html

  51. [59]

    Parthasarathy, Rapid, accurate particle tracking by calculation of radial symmetry centers, Nature Methods 9, 724 (2012)

    R. Parthasarathy, Rapid, accurate particle tracking by calculation of radial symmetry centers, Nature Methods 9, 724 (2012)

    2012

  52. [60]

    Das and S

    B. Das and S. K. Manikandan, Localizing entropy production along non-equilibrium trajectories, arXiv preprint arXiv:2503.20427 (2025)

    2025 arXiv

  53. [61]

    Huang, C

    Y. Huang, C. Liu, B. Miao, and X. Zhou, Entropy pro- duction in non-gaussian active matter: A unified fluc- tuation theorem and deep learning framework, arXiv preprint arXiv:2504.06628 (2025)

    2025

  54. [62]

    Narinder, J

    N. Narinder, J. R. Gomez-Solano, and C. Bechinger, Ac- tive particles in geometrically confined viscoelastic fluids, New Journal of Physics 21, 093058 (2019)

    2019

  55. [63]

    Nakul, S

    U. Nakul, S. Roy, G. Nalupurackal, S. Chakraborty, P. Si- wach, J. Goswami, P. Edwina, S. K. Bajpai, R. Singh, and B. Roy, Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar ac- tive forces, Biomedical optics express 14, 5440 (2023)

    2023

  56. [64]

    T. M. Muenker, G. Knotz, M. Kr¨ uger, and T. Betz, Ac- cessing activity and viscoelastic properties of artificial and living systems from passive measurement, Nature Materials 23, 1283 (2024)

    2024

  57. [65]

    A. Pahi, K. R. Sahoo, B. Das, S. Paul, and A. Banerjee, Simultaneous active and diffusive behaviour of asymmet- ric microclusters in a photophoretic trap, arXiv preprint arXiv:2503.16059 (2025)

    2025 arXiv

  58. [66]

    Gupta, A

    S. Gupta, A. Khan, P. Biswas, K. Mondal, D. Das, S. Sharif, and A. I. Mallick, A combined protocol for isolation of t6ss-positive campylobacter jejuni and as- sessment of interspecies interaction, STAR protocols 3, 101368 (2022)

    2022

  59. [67]

    Seyforth, M

    H. Seyforth, M. Gomez, W. B. Rogers, J. L. Ross, and W. W. Ahmed, Nonequilibrium fluctuations and nonlin- ear response of an active bath, Physical Review Research 4, 023043 (2022)

    2022

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.