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REVIEW 3 major objections 5 minor 95 references

Statistics of Thermal Avalanches in Driven Amorphous Systems

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Thermal avalanches in driven glasses follow non-Poisson waiting-time statistics, yielding closed-form effective temperatures and full counting distributions for avalanche sizes and counts.

desk verdict A genuinely new RFOT-CTRW synthesis for thermal avalanches, but the central results sit on an explicitly admitted and unproven annealed-disorder assumption. read the letter →

arxiv 2603.03550 v1 pith:2NG7CEGH submitted 2026-03-03 cond-mat.dis-nn cond-mat.softcond-mat.stat-mech

Zhiyu Cao , Peter G. Wolynes This is my paper · ORCID
classification cond-mat.dis-nncond-mat.softcond-mat.stat-mech
keywords thermalavalanchesrandomfirst-ordertransitiontheorycontinuous-timewalkfullcountingstatisticseffectivetemperatureagingdynamicsyieldinginstabilitydrivenamorphoussystems
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 argues that mesoscale rearrangements, called thermal avalanches, in driven amorphous materials where thermal noise and mechanical forcing act together can be described by mapping the fluctuating free-energy landscape of string-like rearrangement clusters onto a continuous-time random walk. This mapping yields waiting-time distributions that are non-exponential, reflecting broad energy barriers, and the paper embeds them in a generalized master equation that captures non-Markovian aging dynamics. For quasi-static shear and random shaking protocols, it derives closed-form effective temperatures that exceed the bath temperature and scale in characteristic ways with driving parameters. Using full counting statistics, it further derives the complete distributions of avalanche magnitudes and avalanche counts, including intermediate-time behavior that deviates from the long-time Gaussian limit. If correct, the framework links molecular-scale free-energy landscapes to experimentally measurable avalanche statistics in colloids, cytoskeletal networks, and metallic glasses.

What carries the argument

The central object is the fluctuating string free-energy profile F(L) = phi L + F_in, with slope phi = T Delta s_c + Delta Phi, which is lowered under applied stress. Avalanche growth is a biased random walk on this profile with Metropolis rates truncated by an alpha-relaxation cutoff, producing non-Poisson waiting-time distributions psi±(t). These feed a generalized master equation whose memory kernels are obtained through the Montroll-Weiss formula. A conjugate counting field deforms the avalanche kernel, yielding the full counting-statistics generating function from which all conditional propagators and their tails are extracted.

What would settle it

Measure the waiting-time distribution between successive avalanches in a driven colloidal glass or sheared emulsion (e.g., via particle tracking or acoustic emission) and check whether it matches the non-Poisson form of Eq. (6) with the predicted dependence on the configurational entropy and the alpha-relaxation cutoff. Alternatively, measure the effective temperature via the fluctuation-dissipation ratio as a function of shear ramp rate |alpha|: the paper predicts Teff/T - 1 proportional to exp(-phi R0/|alpha|) for slow ramps, so observing a plateau or a different scaling would invalidate the

Watch

Extended reading notes

Core claim

The central claim is that the stochastic growth of a string-like rearrangement cluster near the yielding instability is equivalent to a one-dimensional biased random walk on a fluctuating free-energy landscape, so that the statistics of complete avalanches are governed by a continuous-time random walk with non-Poisson waiting-time distributions. The paper derives these distributions from Metropolis transition rates with an alpha-relaxation cutoff, then embeds them in a generalized master equation. From large-deviation analysis it obtains effective temperatures via an Einstein-like relation: for shear, Teff/T = 1 + 2 exp(-phi R0/|alpha|)/Delta s_c, and for random shaking, a quadratic correcti

Load-bearing premise

The paper assumes disorder is effectively annealed—each attempted rearrangement samples fresh statistical fluctuations, even for backward moves—so that the renewal structure of the continuous-time random walk (independent waiting times and increments) holds; if the disorder is actually quenched, the waiting-time distributions, generalized master equation, and counting statistics would all need substantial modification.

Editorial extensions

If this is right

  • Effective temperatures are measurable: for slow shear ramps, Teff/T grows exponentially with the inverse ramp rate, and for random shaking it grows quadratically with the temperature difference—predictions testable in colloidal rheology and active-matter experiments.
  • The aging autocorrelation function shows a plateau at short lag times that extends with aging time, then a power-law decay, providing a concrete signature to look for in particle-tracking or rheological data.
  • The full counting statistics predict that at intermediate times the conditional distribution of avalanche size given count is a modified Bessel function, and the distribution of counts given final size has an exponential tail with a slope given by Eq. (40)—quantitative predictions for acoustic-emission or micro-rheology measurements.
  • Geometric amplification factors convert microscopic initiation probabilities into laboratory-observable avalanche-event rates, allowing direct comparison with cytoquake and metallic-glass experiments.

Reading between the lines

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

  • The annealed-disorder assumption may be the first thing to stress-test: if quenched disorder dominates in real systems, the waiting-time distributions and the exponential tails would likely need replacement by correlated or aging-dependent kernels, and the difference could be detected by measuring waiting times in a fixed shear band.
  • The parallel-chain CTRW treatment of random shaking suggests a general mechanism—periodic switching between two temperatures or stress levels—that generically produces an effective temperature quadratic in the control-parameter difference, independent of microscopic details; this could be tested in simulations with different switching protocols.
  • The full counting statistics formalism might transfer directly to other rare-event problems in glassy dynamics, such as counting hopping events in trap models, providing a unified language for counting statistics of structural relaxation.
  • Because stress catalysis appears as a time-dependent tilt of the free-energy landscape, the shear-ramp protocol is formally analogous to a temperature ramp—an equivalence that could let experimentalists use temperature-cycling data to predict shear-ramping responses.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper develops a theory of thermally activated avalanches in driven amorphous systems by combining random first-order transition (RFOT) theory with continuous-time random walk (CTRW) methods. After deriving waiting-time distributions from Metropolis rates on a rugged free-energy landscape (Eqs. 3-6), the authors write a generalized Master equation (Eq. 9) and use it to compute static average statistics, effective temperatures under shear and stochastic shaking protocols (Eqs. 15-18), aging autocorrelation functions (Eqs. 19-32), and full counting statistics of avalanche magnitudes and counts (Eqs. 33-40). The claimed results include closed-form effective-temperature expressions, a non-Gaussian intermediate-time conditional propagator, and an exponential tail in the count distribution. The manuscript also connects the theoretical rates to experimental parameters for cytoquakes and molecular glasses, including an estimate of observable event-rate amplification via a geometric factor.

Significance. If the framework is correct, this paper offers a substantive bridge between molecular-scale RFOT free-energy landscapes and experimentally accessible avalanche statistics in driven disordered materials. The use of non-Poisson waiting times and full counting statistics goes beyond standard mean-field or Gaussian descriptions, and the comparison to cytoquake and colloidal-glass experiments suggests concrete falsifiable predictions. The paper is also transparent in stating its key assumption of annealed disorder, which is a genuine limitation that the authors acknowledge explicitly. The theoretical machinery is ambitious and potentially important for the glass and amorphous-systems community, provided the missing derivations and the technical inconsistency in the counting-field deformation are resolved.

major comments (3)
  1. [Discussion; Eqs. (3)-(4) and (30)-(40)] The CTRW renewal structure requires that each forward/backward event samples fresh, independent fluctuations. However, the transition rates in Eqs. (3)-(4) are explicit functions of the local random forces f_L and f_{L+1}, and in a fixed free-energy landscape the same f_{L+1} controls both L->L+1 and L+1->L. Consecutive reverse moves are therefore correlated, not independent renewals. The Discussion admits this ('effectively annealed disorder assumption, where each event samples fresh fluctuations even if the avalanches were to move backward') but only refers to coarse-graining following ref. [55] without deriving it. This assumption underlies the generalized Master equation, the effective temperature (Eq. 16), the correlation functions (Eqs. 30-32), and the counting statistics (Eqs. 36-40). The central quantitative claims are thus conditional on an approximation whose accuracy near yiel
  2. [Counting statistics, Eqs. (33)-(34)] There is an internal inconsistency in the counting-field deformation. Starting from Eq. (33) with Ktot = K1 + K2 + K3 and deforming only the gain term of K3 to e^{iχ}K3, the Fourier transform gives λ = K1(e^{ik}-1) + K2(e^{-ik}-1) + K3(e^{iχ}e^{ik}-1). The expression in Eq. (34), λ = (K1 + e^{iχ}K3)(e^{ik}-1) + K2(e^{-ik}-1), is different; it corresponds to deforming both the gain and the diagonal loss of the K3 channel differently. Therefore Eq. (34) does not follow from Eq. (33), and the subsequent conditional propagator formulas (Eqs. 35-40) are not derived from the stated master equation. This needs correction.
  3. [Effective temperature, Eqs. (15), (17)-(18)] The closed-form effective-temperature results are deferred to a supplementary information that is not present in this arXiv version. Eq. (15) for v_avg and D, Eq. (17) for the shear-protocol Teff, and Eq. (18) for the shaking-protocol Teff are all central predictions, but their derivations cannot be checked. Without the SI (or an appendix), the paper's headline quantitative claims are unverifiable. Please include these derivations in the revised manuscript.
minor comments (5)
  1. [Figure 3 caption] The caption lists '(a) sc = 1.03kB; (b) sc = 1.13kB; (a) sc = 1.23kB'. The third panel label should likely be '(c)'.
  2. [Section 'A formalism'] The symbol η is introduced as η = Rα/R0, but in Fig. 2 and Figs. 4-6 the parameter η = 0 is used. With η = 0, the lower cutoff in Eq. (6) is at r = 0; while the log-normal factor makes the integral finite, this choice removes the α-relaxation cutoff entirely. A brief justification or comment on the η=0 limit would help.
  3. [Eq. (19)] The autocorrelation function C(tw,t) is defined with a denominator that is the variance of the increment, but the derivation in Eqs. (25)-(32) uses covariance and variance formulas that are not fully aligned in notation. The Laplace-space inversion in Eq. (30) is also written only with a single inverse transform for the denominator; clarifying the two-variable inversion would improve readability.
  4. [Observable event rates] The conversion from P(la|L,t) to an observed probability P_obs uses a geometric amplification factor ηV = Vscan/Vinit. This assumes independent rare events and ignores spatial correlations and the conditioning on a final length L. A short discussion of these assumptions would be useful.
  5. [References] Several statements about 'cytoquakes' and 'effective temperatures' cite experiments, but some of these claims (e.g., Teff one to four orders of magnitude above bath temperature) could benefit from more specific citations in the text rather than only the bibliography.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the RFOT-CTRW predictions follow from prior distinct RFOT results plus explicit CTRW mathematics; the annealed-disorder limitation is a modeling assumption, not a circular step.

full rationale

The paper's derivation chain is self-contained in the sense that none of its target outputs (effective temperatures, autocorrelation functions, counting statistics) is used to calibrate the model. The inputs — R0 from cytoquake experiments, ΔCp, Tg, sc, and the RFOT string parameters — are stated physical/control parameters or prior RFOT constants, not fitted to Teff or P(la|L,t). The logical flow is: Eq. (2) maps the fluctuating string free energy to a biased random walk; Metropolis transition rates (Eqs. (3)-(4)) produce the waiting-time distributions (Eq. (6)); those feed the generalized Master equation (Eq. (9)); large-deviation theory yields Eq. (15) and the effective temperatures Eqs. (17)-(18); full counting statistics deforms the GME kernel to obtain Eq. (34) and the counting distributions Eqs. (36)-(40). Each step is a mathematical consequence of the previous one under explicitly stated assumptions. The Discussion contains the only passage that could be read as a concession: "The present RFOT-CTRW framework has been formulated under an effectively annealed disorder assumption, where each event samples fresh fluctuations even if the avalanches were to move backward." This is a genuine modeling assumption and limits quantitative accuracy near yielding, but it is not circularity: the renewal property is a hypothesis about the disorder ensemble, not a result that has been fitted or renamed. The paper leans heavily on prior Wolynes-group work (e.g., Refs. [22], [31], [55], [56]), but these are earlier results with distinct targets (yield strength, string entropy, secondary-relaxation barriers, random-energy-model dynamics), not the avalanche-statistics outputs claimed here. No uniqueness theorem is imported to forbid alternatives, and no ansatz is smuggled in under a citation while being itself an unsupported choice. Thus the central claims have independent content beyond their inputs.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

All parameters are material or control inputs from prior literature or chosen for illustration; no target dataset is fitted. The calculation leans heavily on RFOT input assumptions, the Gaussian-noise model, and especially the annealed-disorder approximation, which is the most fragile premise.

free parameters (3)
  • R0 (intrinsic transition rate) = 0.01–1 s^-1; 0.01 s^-1 in figures
    Sets the overall time scale for waiting-time distributions and enters the Teff corrections. Chosen from external cytoquake experiments, not fitted to the paper's predicted outputs.
  • η = Rα/R0 (facilitation cutoff ratio) = 0 in all figures
    The α-relaxation cutoff is set to zero, simplifying the waiting-time integrals. This is a modeling choice that affects the shape of ψ±th and the quantitative predictions.
  • ΔCp (configurational heat capacity per particle) = 1 k_B in figures
    Controls the noise width δf and the exponent (Δsc ± ln r)²/(2ΔCp). Chosen for illustration, not fitted to target data.
assumptions (6)
  • domain assumption RFOT free-energy functional Eq. 1 with surface tension σ0 and linear string profile F(L)=ϕL+Fin
    The central rate distributions are derived from this landscape. It is established RFOT theory, but the paper does not re-derive it.
  • domain assumption Gaussian uncorrelated noise f̃ with width δf≈T√ΔCp in Eq. 2
    Maps the free-energy profile to a random walk with independent increments, which is essential for the CTRW waiting-time distributions.
  • ad hoc to paper Annealed disorder: each attempted step samples fresh fluctuations
    Explicitly stated in the Discussion. This ensures the renewal/independent-increment structure; if disorder is quenched, the entire CTRW construction fails.
  • domain assumption Metropolis transition rates with facilitation cutoff Rα (Eqs. 3-4)
    Chooses the functional form of the rates. The cutoff Rα is an input from prior facilitated-dynamics treatments, not derived here.
  • standard math Renewal theory / Montroll-Weiss relations for memory kernels
    Standard CTRW mathematics, used to connect waiting-time distributions to the generalized Master equation.
  • standard math Large-deviation principle and saddle-point asymptotics
    Used to obtain the rate function and Bessel asymptotics in the counting-statistics section.

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Pith. "Pith review of Statistics of Thermal Avalanches in Driven Amorphous Systems." pith.science (2026). https://pith.science/paper/2NG7CEGH

@misc{pith2026260303550,
  author       = {Pith},
  title        = {Pith review of: Statistics of Thermal Avalanches in Driven Amorphous Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2NG7CEGH}},
  note         = {Machine review of arXiv:2603.03550}
}
read the original abstract

Within the framework of the random first-order transition theory of glasses, we discuss the statistics of thermal avalanches, the large scale rearrangements in driven amorphous systems near their instability. Stringy excitations yield nonPoisson waiting time statistics. Embedding these statistics in a generalized Master equation captures the nonMarkovian, aging dynamics of avalanche clusters. We apply this framework to analyze nonequilibrium signatures of thermal avalanches, auto correlation functions and effective temperatures, under both quasi static shear and stochastic shaking protocols. We use full counting statistics to derive the complete distribution of both the avalanche magnitudes and avalanche counts, uncovering the intermediate time behavior.

Figures

Figures reproduced from arXiv: 2603.03550 by the authors.

Figure 1
Figure 1. FIG. 1. The free energy [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Effective temperature [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The simulation results of the aging correlation function [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The conditional distribution of avalanches [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The conditional distribution of avalanches [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The conditional distribution of avalanches [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

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Works this paper leans on

95 extracted references · 1 linked inside Pith

  1. [55]

    J. D. Stevenson and P. G. Wolynes, Nature physics 6, 62 (2010)

    2010

  2. [1]

    Lubchenko and P

    V. Lubchenko and P. G. Wolynes, Annu. Rev. Phys. Chem. 58, 235 (2007)

    2007

  3. [2]

    J. Lin, E. Lerner, A. Rosso, and M. Wyart, Proceedings of the National Academy of Sciences 111, 14382 (2014)

    2014

  4. [3]

    Tahaei, G

    A. Tahaei, G. Biroli, M. Ozawa, M. Popovi´ c, and M. Wyart, Physical Review X 13, 031034 (2023)

    2023

  5. [4]

    Wyart, L

    M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Witten, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 72, 051306 (2005)

    2005

  6. [5]

    Wyart, S

    M. Wyart, S. R. Nagel, and T. A. Witten, Europhysics Letters 72, 486 (2005)

    2005

  7. [6]

    Ozawa, L

    M. Ozawa, L. Berthier, G. Biroli, A. Rosso, and G. Tarjus, Proceedings of the National Academy of Sciences 115, 6656 (2018)

    2018

  8. [7]

    Chauve, T

    P. Chauve, T. Giamarchi, and P. Le Doussal, Physical Review B 62, 6241 (2000)

    2000

Show all 95 references
  1. [8]

    T. W. De Geus, A. Rosso, and M. Wyart, Physical Review E 111, L013503 (2025)

    2025

  2. [9]

    Durin, V

    G. Durin, V. M. Schimmenti, M. Baiesi, A. Casiraghi, A. Magni, L. Herrera-Diez, D. Ravelosona, L. Foini, and A. Rosso, Physical Review B 110, L020405 (2024)

    2024

  3. [10]

    E. E. Ferrero, L. Foini, T. Giamarchi, A. B. Kolton, and A. Rosso, Annual Review of Condensed Matter Physics 12, 111 (2021)

    2021

  4. [11]

    D. J. Korchinski, D. Shohat, Y. Lahini, and M. Wyart, arXiv preprint arXiv:2409.17415 (2024)

    2024 arXiv

  5. [12]

    E. Zhou, X. Trepat, C. Park, G. Lenormand, M. Oliver, S. Mijailovich, C. Hardin, D. Weitz, J. Butler, and J. Fredberg, Proceedings of the National Academy of Sciences 106, 10632 (2009)

    2009

  6. [13]

    A. M. Alencar, M. S. A. Ferraz, C. Y. Park, E. Millet, X. Trepat, J. J. Fredberg, and J. P. Butler, Soft matter 12, 8506 (2016)

    2016

  7. [14]

    Liman, C

    J. Liman, C. Bueno, Y. Eliaz, N. P. Schafer, M. N. Waxham, P. G. Wolynes, H. Levine, and M. S. Cheung, Proceedings of the National Academy of Sciences 117, 10825 (2020)

    2020

  8. [15]

    Floyd, H

    C. Floyd, H. Levine, C. Jarzynski, and G. A. Papoian, Proceedings of the National Academy of Sciences 118, e2110239118 (2021)

    2021

  9. [16]

    Wang and P

    S. Wang and P. G. Wolynes, Proceedings of the National Academy of Sciences 109, 6446 (2012)

    2012

  10. [17]

    Bouchaud and E

    J.-P. Bouchaud and E. Pitard, The European Physical Journal E 6, 231 (2001)

    2001

  11. [18]

    Angelini, L

    R. Angelini, L. Zulian, A. Fluerasu, A. Madsen, G. Ruocco, and B. Ruzicka, Soft Matter 9, 10955 (2013)

    2013

  12. [19]

    Gabriel, T

    J. Gabriel, T. Blochowicz, and B. St¨ uhn, The Journal of chemical physics 142 (2015)

    2015

  13. [20]

    Q. Li, X. Peng, and G. B. McKenna, Soft matter 15, 2336 (2019)

    2019

  14. [21]

    Z. Cao, C. Du, Z. Hou, and P. G. Wolynes, Nature Communications 16, 11085 (2025)

    2025

  15. [22]

    Wisitsorasak and P

    A. Wisitsorasak and P. G. Wolynes, Proceedings of the National Academy of Sciences 109, 16068 (2012)

    2012

  16. [23]

    Wisitsorasak and P

    A. Wisitsorasak and P. G. Wolynes, Proceedings of the National Academy of Sciences 114, 1287 (2017)

    2017

  17. [24]

    W. Kob, C. Donati, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Physical review letters 79, 2827 (1997)

    1997

  18. [25]

    Donati, J

    C. Donati, J. F. Douglas, W. Kob, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Physical review letters 80, 2338 (1998)

    1998

  19. [26]

    Donati, S

    C. Donati, S. C. Glotzer, P. H. Poole, W. Kob, and S. J. Plimpton, Physical Review E 60, 3107 (1999)

    1999

  20. [27]

    Gebremichael, M

    Y. Gebremichael, M. Vogel, and S. C. Glotzer, The Journal of chemical physics 120, 4415 (2004)

    2004

  21. [28]

    E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, Science 287, 627 (2000)

    2000

  22. [29]

    S. A. Reinsberg, A. Heuer, B. Doliwa, H. Zimmermann, and H. W. Spiess, Journal of non-crystalline solids 307, 208 (2002)

    2002

  23. [30]

    Langer and A

    J. Langer and A. Lema ˆ ıtre, Physical review letters94, 175701 (2005)

    2005

  24. [31]

    J. D. Stevenson, J. Schmalian, and P. G. Wolynes, Nature Physics 2, 268 (2006)

    2006

  25. [32]

    S. M. Bhattacharyya, B. Bagchi, and P. G. Wolynes, Proceedings of the National Academy of Sciences 105, 16077 (2008). 18

    2008

  26. [33]

    Lubchenko and P

    V. Lubchenko and P. G. Wolynes, The Journal of Physical Chemistry B 122, 3280 (2017)

    2017

  27. [34]

    Zhang, S

    G. Zhang, S. A. Ridout, and A. J. Liu, Physical Review X 11, 041019 (2021)

    2021

  28. [35]

    J. C. Dyre, Reviews of modern physics 78, 953 (2006)

    2006

  29. [36]

    Picard, A

    G. Picard, A. Ajdari, F. Lequeux, and L. Bocquet, The European Physical Journal E 15, 371 (2004)

    2004

  30. [37]

    C. E. Maloney and A. Lemaitre, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 74, 016118 (2006)

    2006

  31. [38]

    Lema ˆ ıtre, Physical review letters113, 245702 (2014)

    A. Lema ˆ ıtre, Physical review letters113, 245702 (2014)

    2014

  32. [39]

    Bocquet, A

    L. Bocquet, A. Colin, and A. Ajdari, Physical review letters 103, 036001 (2009)

    2009

  33. [40]

    Lubchenko, Proceedings of the National Academy of Sciences 106, 11506 (2009)

    V. Lubchenko, Proceedings of the National Academy of Sciences 106, 11506 (2009)

    2009

  34. [41]

    Rabochiy and V

    P. Rabochiy and V. Lubchenko, The Journal of Physical Chemistry B 116, 5729 (2012)

    2012

  35. [42]

    Xia and P

    X. Xia and P. G. Wolynes, Physical Review Letters 86, 5526 (2001)

    2001

  36. [43]

    Wisitsorasak and P

    A. Wisitsorasak and P. G. Wolynes, The Journal of Physical Chemistry B 118, 7835 (2014)

    2014

  37. [44]

    L. S. Levitov and G. B. Lesovik, JETP LETTERS C/C OF PIS’MA V ZHURNAL EKSPERIMENTAL’NOI TEORETICH- ESKOI FIZIKI 58, 230 (1993)

    1993

  38. [45]

    L. S. Levitov, H. Lee, and G. B. Lesovik, Journal of Mathematical Physics 37, 4845 (1996)

    1996

  39. [46]

    Y. V. Nazarov, Quantum noise in mesoscopic physics, Vol. 97 (Springer Science & Business Media, 2012)

    2012

  40. [47]

    Bagrets and Y

    D. Bagrets and Y. V. Nazarov, Physical Review B 67, 085316 (2003)

    2003

  41. [48]

    Flindt, T

    C. Flindt, T. Novotn` y, A. Braggio, M. Sassetti, and A.-P. Jauho, Physical review letters 100, 150601 (2008)

    2008

  42. [49]

    Braggio, J

    A. Braggio, J. K¨ onig, and R. Fazio, Physical review letters 96, 026805 (2006)

    2006

  43. [50]

    T. R. Kirkpatrick, D. Thirumalai, and P. G. Wolynes, Physical Review A 40, 1045 (1989)

    1989

  44. [51]

    Xia and P

    X. Xia and P. G. Wolynes, Proceedings of the National Academy of Sciences 97, 2990 (2000)

    2000

  45. [52]

    Richert and C

    R. Richert and C. Angell, The Journal of chemical physics 108, 9016 (1998)

    1998

  46. [53]

    J. D. Stevenson and P. G. Wolynes, The Journal of Physical Chemistry B 109, 15093 (2005)

    2005

  47. [54]

    Lubchenko and P

    V. Lubchenko and P. G. Wolynes, The Journal of chemical physics 121, 2852 (2004)

    2004

  48. [56]

    J. D. Bryngelson and P. G. Wolynes, The Journal of Physical Chemistry 93, 6902 (1989)

    1989

  49. [57]

    D. Cox, H. Miller, G. Weiss, and K. Shuler, The theory of stochastic processes (1966)

    1966

  50. [58]

    Feller, An introduction to probability theory and its applications, Volume 2, Vol

    W. Feller, An introduction to probability theory and its applications, Volume 2, Vol. 81 (John Wiley & Sons, 1991)

    1991

  51. [59]

    Parisi, I

    G. Parisi, I. Procaccia, C. Rainone, and M. Singh, Proceedings of the National Academy of Sciences 114, 5577 (2017)

    2017

  52. [60]

    Coussot, Q

    P. Coussot, Q. D. Nguyen, H. Huynh, and D. Bonn, Physical review letters 88, 175501 (2002)

    2002

  53. [61]

    Agoritsas, E

    E. Agoritsas, E. Bertin, K. Martens, and J.-L. Barrat, The European Physical Journal E 38, 1 (2015)

    2015

  54. [62]

    Nicolas, E

    A. Nicolas, E. E. Ferrero, K. Martens, and J.-L. Barrat, Reviews of Modern Physics 90, 045006 (2018)

    2018

  55. [63]

    E. Sanz, C. Valeriani, E. Zaccarelli, W. C. Poon, M. E. Cates, and P. N. Pusey, Proceedings of the National Academy of Sciences 111, 75 (2014)

    2014

  56. [64]

    Gibaud, N

    T. Gibaud, N. Dag` es, P. Lidon, G. Jung, L. C. Ahour´ e, M. Sztucki, A. Poulesquen, N. Hengl, F. Pignon, and S. Manneville, Physical Review X 10, 011028 (2020)

    2020

  57. [65]

    M. K. Nandi and S. M. Bhattacharyya, Journal of Physics: Condensed Matter 32, 064001 (2019)

    2019

  58. [66]

    Seki, Journal of Statistical Mechanics: Theory and Experiment 2023, 123207 (2023)

    K. Seki, Journal of Statistical Mechanics: Theory and Experiment 2023, 123207 (2023)

    2023

  59. [67]

    P. G. Wolynes, Proceedings of the National Academy of Sciences 106, 1353 (2009)

    2009

  60. [68]

    Berthier and G

    L. Berthier and G. Biroli, Reviews of modern physics 83, 587 (2011)

    2011

  61. [69]

    R. N. Chacko, F. P. Landes, G. Biroli, O. Dauchot, A. J. Liu, and D. R. Reichman, Physical Review X 14, 031012 (2024). 19

    2024

  62. [70]

    Flomenbom and J

    O. Flomenbom and J. Klafter, Physical review letters 95, 098105 (2005)

    2005

  63. [71]

    E. B. Stukalin and A. B. Kolomeisky, The Journal of chemical physics 124 (2006)

    2006

  64. [72]

    Teimouri and A

    H. Teimouri and A. B. Kolomeisky, The Journal of Chemical Physics 138 (2013)

    2013

  65. [73]

    Touchette, Physics Reports 478, 1 (2009)

    H. Touchette, Physics Reports 478, 1 (2009)

    2009

  66. [74]

    Akimoto, A

    T. Akimoto, A. G. Cherstvy, and R. Metzler, Physical Review E 98, 022105 (2018)

    2018

  67. [75]

    Y. He, S. Burov, R. Metzler, and E. Barkai, Physical Review Letters 101, 058101 (2008)

    2008

  68. [76]

    R. Hou, A. G. Cherstvy, R. Metzler, and T. Akimoto, Physical Chemistry Chemical Physics 20, 20827 (2018)

    2018

  69. [77]

    K. Seki, N. Muramatsu, T. Miura, and T. Ikoma, The Journal of Chemical Physics 158 (2023)

    2023

  70. [78]

    Hatano and S.-i

    T. Hatano and S.-i. Sasa, Physical review letters 86, 3463 (2001)

    2001

  71. [79]

    Harada and S.-i

    T. Harada and S.-i. Sasa, Physical review letters 95, 130602 (2005)

    2005

  72. [80]

    Celani, S

    A. Celani, S. Bo, R. Eichhorn, and E. Aurell, Physical review letters 109, 260603 (2012)

    2012

  73. [81]

    Shen and P

    T. Shen and P. G. Wolynes, Proceedings of the National Academy of Sciences 101, 8547 (2004)

    2004

  74. [82]

    Wang and P

    S. Wang and P. G. Wolynes, The Journal of chemical physics 135 (2011)

    2011

  75. [83]

    Fritzsche, A

    M. Fritzsche, A. Lewalle, T. Duke, K. Kruse, and G. Charras, Molecular biology of the cell 24, 757 (2013)

    2013

  76. [84]

    D. Loi, S. Mossa, and L. F. Cugliandolo, Soft Matter 7, 3726 (2011)

    2011

  77. [85]

    D. Loi, S. Mossa, and L. F. Cugliandolo, Soft Matter 7, 10193 (2011)

    2011

  78. [86]

    Mizuno, C

    D. Mizuno, C. Tardin, C. F. Schmidt, and F. C. MacKintosh, Science 315, 370 (2007)

    2007

  79. [87]

    Ginot, I

    F. Ginot, I. Theurkauff, D. Levis, C. Ybert, L. Bocquet, L. Berthier, and C. Cottin-Bizonne, Physical Review X 5, 011004 (2015)

    2015

  80. [88]

    Palacci, C

    J. Palacci, C. Cottin-Bizonne, C. Ybert, and L. Bocquet, Physical Review Letters 105, 088304 (2010)

    2010

  81. [89]

    D´ emery and´E

    V. D´ emery and´E. Fodor, Journal of Statistical Mechanics: Theory and Experiment 2019, 033202 (2019)

    2019

  82. [90]

    Sharaf and J

    M. Sharaf and J. Mark, Rubber Chemistry and Technology 53, 982 (1980)

    1980

  83. [91]

    Verberk and M

    R. Verberk and M. Orrit, The Journal of Chemical Physics 119, 2214 (2003)

    2003

  84. [92]

    Margolin and E

    G. Margolin and E. Barkai, The Journal of chemical physics 121, 1566 (2004)

    2004

  85. [93]

    J. B. Witkoskie and J. Cao, The Journal of chemical physics 125 (2006)

    2006

  86. [94]

    Cipelletti, S

    L. Cipelletti, S. Manley, R. Ball, and D. Weitz, Physical review letters 84, 2275 (2000)

    2000

  87. [95]

    B. Ruta, Y. Chushkin, G. Monaco, L. Cipelletti, E. Pineda, P. Bruna, V. Giordano, and M. Gonzalez-Silveira, Physical review letters 109, 165701 (2012)

    2012

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