Pith. sign in

REVIEW 2 major objections 3 minor 55 references

An altruistic resource-sharing mechanism for synchronization: The energy-speed-accuracy tradeoff

T0 review · 2 major / 3 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read Resource-mediated synchronization obeys the same energy-speed-accuracy tradeoff as direct coupling.

desk verdict Elegant analytical model of resource-sharing synchronization, but the claimed universal ESA law rests on an approximation that the SI admits fails in the scarce-resource regime where the law matters most. read the letter →

arxiv 2502.02242 v1 pith:Z5JOFOEV submitted 2025-02-04 cond-mat.stat-mech physics.bio-ph

Dongliang Zhang , Yuansheng Cao , Qi Ouyang , Yuhai Tu This is my paper · ORCID
classification cond-mat.stat-mechphysics.bio-ph
keywords synchronizationaltruisticresourcesharingenergy-speed-accuracytradeoffFokker-PlanckequationthermodynamicuncertaintyrelationKaiABCcircadianclockParetofrontnonequilibriumthermodynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to establish that synchronization via shared, limited resources—rather than direct pairwise coupling—obeys a universal energy-speed-accuracy (ESA) tradeoff. It constructs a minimal thermodynamically consistent model in which agents advance only when bound to a shared activator, and more advanced agents bind the activator less well, creating an altruistic negative feedback that pulls agents together. Solving the resulting Fokker-Planck equation analytically, the authors find that this mechanism necessarily dissipates energy beyond the cost of driving individual agents, and that the synchronization error falls as the inverse product of the two dissipation channels. For a fixed dissipation budget, speed and accuracy trade off along a Pareto front traversed by resource scarcity; increasing dissipation pushes the front outward. If correct, the result gives a quantitative, testable design principle for biological clocks and other resource-mediated synchronizing systems.

What carries the argument

The central object is the steady-state traveling wave $\rho_s(u) = \frac{1}{Z}(e^{\alpha u}+1)\exp[e_p(1-A_t)u - \frac{A_t e_p}{\alpha}e^{\alpha u}]$ with $u = x - vt$, arising from the Fokker-Planck equation for the density $\rho(x,t)$ together with the occupancy function $p(x) = g/(e^{\alpha(x-x_0)}+1)$ fixed by activator conservation $\int p(x)\rho(x,t)\,dx = m_t$. The wave is what makes the problem solvable: it converts the joint agent-resource dynamics into a one-dimensional effective potential $E_{\mathrm{eff}}(u) = -\ln \rho_s(u)$, whose curvature directly gives the synchronization error $\sigma^2$. The dissipative cycle behind the model is the flux loop combining processive steps and differential binding, quantified by $\Gamma_l = e^{(2e_p+\alpha)\Delta x}$, and the dissipation rate is computed from the probability flux $J = v\rho$ via $\dot{W} = \int \frac{J^2}{kp\rho}\,dx$. The central identity is the ESA relation $\sigma^2 \approx 1/(W_0 W_s)$ for weak sharing, with $W_0=e_p$ and $W_s=(1-A_t)\alpha$, which organizes all the parametric dependencies.

What would settle it

Measure the synchronization variance $\sigma^2$ and per-agent dissipation rate $\dot{W}$ in a resource-sharing system (for example, KaiC hexamers with titrated KaiA) while varying the resource abundance $A_t$; if, at fixed $e_p$ and $A_t$, a plot of $\ln \sigma^2$ against $\ln W_s$ does not follow a line of slope $-1$ in the weak-sharing regime, or if the speed–accuracy Pareto front does not move outward with increasing $\dot{W}$, the central ESA claim is falsified.

Watch

Extended reading notes

Core claim

The paper claims that synchronization through altruistic resource sharing is a genuine out-of-equilibrium process whose energy cost is set by the same formula as the synchronization accuracy it buys. In the model, $N$ agents advance only while bound to a shared activator; an agent's binding affinity falls exponentially with advancement ($E(x)=\alpha x$), so laggards capture more resources, creating negative feedback. The resulting cycle has rate-product ratio $\Gamma_l = e^{(2e_p+\alpha)\Delta x} \neq 1$, so it breaks detailed balance and dissipates free energy at rate $\dot{W} = v[e_p + (1-A_t)\alpha]$ per agent, split into a processive cost $\dot{W}_0 = v e_p$ and a synchronization cost $\dot{W}_s = v(1-A_t)\alpha$. The steady-state traveling wave has variance $\sigma^2 \approx 1/(W_s W_0)$ in the weak-sharing regime ($W_s = (1-A_t)\alpha$, $W_0 = e_p$), and saturates at $\sigma^2_s = (2-A_t)A_t/[e_p^2(1-A_t)^2]$ for strong sharing. The authors conclude that for fixed dissipation, achievable speed and accuracy form a Pareto front parameterized by resource scarcity $A_t$, that higher dissipation pushes the front outward, and that the same inverse $\sigma^2$–$W_s$ law holds in the direct pairwise-interaction mechanism, suggesting a mechanism-independent energy-speed-accuracy relation.

Load-bearing premise

The derivations all assume free activators are negligible and binding is fast, so the occupancy $p(x)$ is a fixed saturating function of the wave coordinate and the population advances as a constant-speed traveling wave; when the wave approaches the point where the free-activator fraction grows, the effective resource abundance $A_t$ drops, the speed is no longer constant, and the central ESA formulas are not derived.

Editorial extensions

If this is right

  • For fixed dissipation, resource scarcity alone moves a system along the speed–accuracy Pareto front: scarcer resources give slower but more precise synchronization, and more abundant resources give faster but noisier synchronization.
  • The synchronization error obeys $\sigma^2 \approx 1/(W_0 W_s)$ in the weak-sharing regime, so accuracy can be purchased by either stronger differential binding (larger $\alpha$) or stronger processive drive (larger $e_p$), at equal per-unit-length energy cost.
  • In the strong-sharing limit the population never fully synchronizes: only the fraction $1-A_t$ of agents sits in a delta-function synchronized core unless $A_t \to 0$, so perfect synchronization requires both $\alpha \to \infty$ and vanishing resource abundance.
  • The same inverse accuracy–dissipation law appears in the direct pairwise-interaction mechanism, so the energy-speed-accuracy relation is a candidate universal property of molecular synchronization rather than an artifact of either interaction geometry.
  • Thermodynamic uncertainty relation estimates based on a single agent's displacement current undercount the true dissipation of this collective process, so TUR-style energetic bounds should be read as loose lower bounds for resource-mediated synchronization.

Reading between the lines

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

  • The authors leave implicit that the predicted collapse of $\sigma^2$ against $W_s$ at fixed $e_p$ and $A_t$ is a direct experimental signature; measuring phase variance and ATP consumption in a KaiABC assay would test the ESA relation without resolving individual binding events.
  • If the adiabatic extension to nonlinear binding energies $E(x)$ holds, a design rule follows: a resource-sharing synchronizer needs $E(x)$ to grow at least linearly with advancement, so engineered binding landscapes with sublinear growth should lose synchronization as the wave advances—an experiment one could run with mutated KaiA/KaiC.
  • The TUR discrepancy found here likely generalizes: local-flux thermodynamic uncertainty bounds may systematically miss collective resource-mediated dissipation, so energetic estimates from single-agent trajectories in other active systems should be treated as lower bounds.
  • A synthetic reconstitution with purified KaiC hexamers and titrated KaiA could directly map the predicted speed–accuracy Pareto front at fixed dissipation by varying total KaiA concentration and measuring oscillation coherence and ATP consumption.
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

2 major / 3 minor

Summary. This paper introduces a minimal thermodynamically consistent model for synchronization through altruistic resource sharing (ARS), in which agents advance only when bound to a shared activator and a more advanced agent has reduced binding affinity. In the thermodynamic limit, the authors find an analytic traveling-wave solution and derive closed-form expressions for the synchronization error σ^2 (Eqs. 7 and 9) and the dissipation rate (Eq. 11), leading to the energy-speed-accuracy relation (Eq. 12): σ^2 ≈ 1/(W_s W_0) in the weak-sharing regime and a saturation value for strong sharing. They construct a Pareto surface for the minimum dissipation required for given speed and accuracy (Fig. 3), claim the same ESA relation holds as in the direct pairwise-interaction mechanism, compare with the thermodynamic uncertainty relation, and discuss implications for the KaiABC clock.

Significance. If the central claim is correct, the paper establishes a quantitative, mechanism-independent tradeoff between energy dissipation, synchronization speed, and accuracy for indirect resource-mediated interactions, complementing the authors' earlier direct-interaction result. The analytical solution is a strength, as are the explicit dissipation formula and the Pareto-front construction; the manuscript also contains a useful warning about the limits of TUR for this problem. The derivation is internally consistent and the model has no ad-hoc fitting parameters. However, the validity of the central claim is conditional on an approximation whose breakdown is acknowledged in the SI, in precisely the parameter regime used for the high-accuracy branch of the Pareto front. The paper's value therefore depends on how far the analysis can be extended beyond the no-free-activator idealization.

major comments (2)
  1. [The thermodynamic limit; SI 'The effect of ignoring free activators'] The traveling-wave solution (main-text Eq. 6) and the ESA relations (Eqs. 11-12) are derived under the assumption that free activators can be neglected, e^{E(x)} << 1. However, for A_t < 1/2 the wave peak u_m given by Eq. 20 is positive, so e^{α u_m} > 1 at the center of the distribution. For example, with A_t = 0.4, e_p = 8, and α = 8, Eq. 20 gives e^{α u_m} ≈ 3.44; for A_t = 0.01 the value is orders of magnitude larger. Thus the probability mass is concentrated in the region where the no-free approximation is not controlled, and this is exactly the scarce-resource regime that generates the high-accuracy branch of the Pareto front in Fig. 3. The SI itself states that when the wave approaches x0 the free fraction R grows, A_eff = A_t(1-R) drops, and the velocity v = k e_p A_eff is no longer constant, so Eqs. 11-12 are not derived there. Since the central claim of a universal ESA relation depends on these branches, the manuscript needs either an extension of the solution that includes free activators or an explicit statement of the parameter regime in which the claims hold.
  2. [The thermodynamic limit, Eqs. 8-9] The strong-sharing limit used for the saturation branch also violates the no-free-activator approximation. As α → ∞, Eq. 20 gives u_m → ∞, meaning the wave peak moves to arbitrarily large positive u, where e^{α u_m} → ∞ and free activators dominate. The δ-function component at u = 0 in Eq. 8 sits at e^{E} = 1, not e^{E} << 1. Consequently, the saturation variance σ_s^2 in Eq. 9 and the second line of Eq. 12 are derived in a limit that is outside the controlled regime of the model, and the claimed universality of the ESA relation is not established for this branch either.
minor comments (3)
  1. [Fig. 2 and surrounding text] The sentence 'Direct numerical simulations show that σ^2 decreases with α' does not specify the simulated equations; please state whether the full binding-unbinding dynamics or the approximate Fokker-Planck equation (4) with p(x) fixed by the no-free form was integrated, and if the latter, note that it does not test the free-activator approximation.
  2. [TUR discussion, Eq. (14)] The statement that the result 'reflects the limitation of using TUR for specific individual observables' is misleading because TUR is a lower bound by construction, so Ẇ_TUR < Ẇ for finite T is expected; suggest rephrasing to say that the chosen observable does not saturate the TUR bound.
  3. [SI, after Eq. (20)] The sentence 'For simplicity we choose u = 0 in main text' should read 'we choose u0 = 0 in the main text' to distinguish the binding-energy reference point from the integration variable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ESA relations follow from the model's own analytically solved traveling wave, with no fitted inputs and no load-bearing self-citation.

full rationale

The derivation chain is self-contained. The occupancy p(x)=g/(e^{α(x−x0)}+1) follows from the canonical partition function over activator arrangements (SI Eqs. 12–17), and the traveling-wave density ρs(u) in Eq. 6 is obtained by integrating the Fokker-Planck equation (Eq. 4) together with the resource-conservation constraint (Eq. 5). The variance formulas (Eqs. 7 and 9) are asymptotic expansions of this derived ρs, not fits. The dissipation rate (Eq. 10) is a standard flux formula; substituting the traveling wave gives Eq. 11, and Eq. 12 is an algebraic rewriting of Eqs. 7, 9, and 11 after defining Ws=(1−At)α and W0=ep. No parameter is fitted to the target quantities, and no equation reduces to an input by construction. The comparison with the pairwise-interaction model cites the authors' prior Nature Physics paper, but that is an independently derived external model used as a benchmark, not as an input to the ARS derivation; it is therefore not a load-bearing self-citation. The SI caveat about free activators (SI, 'The effect of ignoring free activators': 'When x approaches x0, R dramatically increases and Aeff quickly drops, which prevents the agents from moving further') is a genuine domain-of-validity limitation on the traveling-wave and ESA formulas, but it is not a circularity: it does not make the derived equations equivalent to their assumptions, although it does mean the advertised 1/(WsW0) law is conditional on the e^{E(x)}≪1 regime being maintained.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

No parameters are fitted to experimental data; the central tradeoff is parametric. The main extra assumptions beyond standard stochastic thermodynamics are the fast-binding/no-free-activator regime and the linear differential binding energy. No new physical entities are postulated.

free parameters (5)
  • e_p (processive driving force per unit length) = not fitted, swept
    Sets the bias of the random walk and the baseline dissipation W0=e_p; central to speed v=k e_p A_t and to the ESA relation.
  • alpha (differential binding energy slope) = not fitted, swept
    Controls the negative feedback and the synchronization cost W_s=(1-A_t)alpha; varied to construct the Pareto front.
  • A_t (relative resource abundance m_t/g) = not fitted, swept
    Resource scarcity relative to demand; the key control parameter that moves the speed-accuracy front.
  • g (maximum activator occupancy per agent) = not fitted, set to 1 in Fig.3 scalings
    Appears in the maximum speed v_m=(k g W*)^{1/2} and in p(x); does not affect the shape of Eq.12.
  • k (processive stepping rate) = not fitted, sets timescale
    Overall rate scale; affects W through v=k e_p g A_t.
assumptions (6)
  • domain assumption Activator binding arrangements follow a canonical (detailed-balance) distribution with maximum occupancy g per agent (SI Eqs.12-16).
    Gives p(x)=g/(e^{alpha(x-x0)}+1); assumes binding equilibrates rapidly and free activators can be ignored.
  • domain assumption Fast binding limit q much greater than k, so occupancies relax instantaneously to p_i and the reduced Fokker-Planck Eq.2/4 holds.
    Main text after Eq.2; no error estimate for finite q.
  • domain assumption No free activators: e^{E(x)} much less than 1, so all M activators are bound and the integral p rho dx = m_t is constant.
    Stated in the simplest case and the SI; the SI admits it fails as the wave approaches x0.
  • domain assumption Thermodynamic limit with finite m_t=M/N and traveling-wave ansatz rho(x,t)=rho_s(x-vt).
    Used to derive Eqs.4-6 and the constant speed v=k e_p m_t.
  • standard math Continuum limit Delta x to 0 with rescaling k(Delta x)^2 to k and local detailed balance rates.
    Standard Fokker-Planck coarse-graining; stated in footnote [23].
  • domain assumption Linear binding energy E(x)=alpha x; nonlinear E(x) treated only adiabatically in the SI.
    Simplifies to a Fermi occupancy; the SI argues it approximates slowly varying E(x).

how reviews work

0 comments
Cite this review

Pith. "Pith review of An altruistic resource-sharing mechanism for synchronization: The energy-speed-accuracy tradeoff." pith.science (2026). https://pith.science/paper/Z5JOFOEV

@misc{pith2026250202242,
  author       = {Pith},
  title        = {Pith review of: An altruistic resource-sharing mechanism for synchronization: The energy-speed-accuracy tradeoff},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z5JOFOEV}},
  note         = {Machine review of arXiv:2502.02242}
}
read the original abstract

Synchronization among a group of active agents is ubiquitous in nature. Although synchronization based on direct interactions between agents described by the Kuramoto model is well understood, the other general mechanism based on indirect interactions among agents sharing limited resources are less known. Here, we propose a minimal thermodynamically consistent model for the altruistic resource-sharing (ARS) mechanism wherein resources are needed for individual agent to advance but a more advanced agent has a lower competence to obtain resources. We show that while differential competence in ARS mechanism provides a negative feedback leading to synchronization it also breaks detailed balance and thus requires additional energy dissipation besides the cost of driving individual agents. By solving the model analytically, our study reveals a general tradeoff relation between the total energy dissipation rate and the two key performance measures of the system: average speed and synchronization accuracy. For a fixed dissipation rate, there is a distinct speed-accuracy Pareto front traversed by the scarcity of resources: scarcer resources lead to slower speed but more accurate synchronization. Increasing energy dissipation eases this tradeoff by pushing the speed-accuracy Pareto front outwards. The connections of our work to realistic biological systems such as the KaiABC system in cyanobacterial circadian clock and other theoretical results based on thermodynamic uncertainty relation are also discussed.

Figures

Figures reproduced from arXiv: 2502.02242 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of the simplest model ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Dependence of synchronization on key parameters. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Energy-speed-accuracy tradeoff. (A) The Pareto [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 50 canonical work pages

  1. [1]

    M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Reviews of modern physics 85, 1143 (2013)

    2013

  2. [2]

    Bialek, A

    W. Bialek, A. Cavagna, I. Giardina, T. Mora, E. Sil- vestri, M. Viale, and A. M. Walczak, Proceedings of the National Academy of Sciences 109, 4786 (2012)

    work page 2012

  3. [3]

    Toner and Y

    J. Toner and Y. Tu, Physical review E 58, 4828 (1998)

    1998

  4. [4]

    Elgeti, R

    J. Elgeti, R. G. Winkler, and G. Gompper, Reports on progress in physics 78, 056601 (2015)

    2015

  5. [5]

    Yu and Y

    Q. Yu and Y. Tu, Physical review letters 129, 278001 (2022)

    work page 2022

  6. [7]

    J. A. Acebr´ on, L. L. Bonilla, C. J. P´ erez Vicente, F. Ri- tort, and R. Spigler, Reviews of modern physics 77, 137 (2005)

    work page 2005

  7. [8]

    Tailleur, G

    J. Tailleur, G. Gompper, M. C. Marchetti, J. M. Yeo- mans, and C. Salomon, Active Matter and Nonequi- librium Statistical Physics: Lecture Notes of the Les Houches Summer School: Volume 112, September 2018 , Vol. 112 (Oxford University Press, 2022)

    work page 2018

  8. [9]

    J. S. van Zon, D. K. Lubensky, P. R. Altena, and P. R. 6 ten Wolde, Proceedings of the National Academy of Sci- ences 104, 7420 (2007)

    work page 2007

Show all 55 references
  1. [10]

    Nagai, T

    T. Nagai, T. P. Terada, and M. Sasai, Biophysical jour- nal 98, 2469 (2010)

    2010

  2. [11]

    Paijmans, D

    J. Paijmans, D. K. Lubensky, and P. R. ten Wolde, PLoS computational biology 13, e1005415 (2017)

    2017

  3. [12]

    Kageyama, T

    H. Kageyama, T. Nishiwaki, M. Nakajima, H. Iwasaki, T. Oyama, and T. Kondo, Molecular cell 23, 161 (2006)

    2006

  4. [13]

    Emberly and N

    E. Emberly and N. S. Wingreen, Physical review letters 96, 038303 (2006)

    2006

  5. [14]

    H. Ito, H. Kageyama, M. Mutsuda, M. Nakajima, T. Oyama, and T. Kondo, Nature structural & molecular biology 14, 1084 (2007)

    2007

  6. [15]

    T. Mori, D. R. Williams, M. O. Byrne, X. Qin, M. Egli, H. S. Mchaourab, P. L. Stewart, and C. H. Johnson, PLoS biology 5, e93 (2007)

    2007

  7. [16]

    M. Yoda, K. Eguchi, T. P. Terada, and M. Sasai, PloS one 2, e408 (2007)

    2007

  8. [17]

    Eguchi, M

    K. Eguchi, M. Yoda, T. P. Terada, and M. Sasai, Bio- physical journal 95, 1773 (2008)

    2008

  9. [18]

    M. J. Rust, J. S. Markson, W. S. Lane, D. S. Fisher, and E. K. O’shea, Science 318, 809 (2007)

    2007

  10. [19]

    Ma and R

    L. Ma and R. Ranganathan, PLoS One 7, e42581 (2012)

    2012

  11. [20]

    J. Lin, J. Chew, U. Chockanathan, and M. J. Rust, Proceedings of the National Academy of Sciences 111, E3937 (2014)

    2014

  12. [21]

    A. K. Behera, C. d. Junco, and S. Vaikuntanathan, The Journal of Physical Chemistry B 125, 11179 (2021)

    2021

  13. [22]

    T. Mori, S. Sugiyama, M. Byrne, C. H. Johnson, T. Uchi- hashi, and T. Ando, Nature Communications 9, 3245 (2018)

    2018

  14. [23]

    We did rescaling k(∆ x)2 → k in the continuum limit

  15. [24]

    Tom´ e and M

    T. Tom´ e and M. J. de Oliveira, Physical review E 82, 021120 (2010)

    2010

  16. [25]

    Zhang and Q

    D. Zhang and Q. Ouyang, Entropy 23, 271 (2021)

    2021

  17. [26]

    e∗ p and α ∗ can be determined from A∗ t and the targeted performance ( v, A )

  18. [27]

    A. C. Barato and U. Seifert, Physical review letters 114, 158101 (2015)

    2015

  19. [29]

    S. Lee, C. Hyeon, and J. Jo, Physical Review E 98, 032119 (2018)

    2018

  20. [30]

    Dieball and A

    C. Dieball and A. Godec, Physical Review Letters 130, 087101 (2023)

    2023

  21. [31]

    Tu and W.-J

    Y. Tu and W.-J. Rappel, Annual Review of Condensed Matter Physics 9, 183 (2018)

    2018

  22. [32]

    G. Lan, P. Sartori, S. Neumann, V. Sourjik, and Y. Tu, Nature physics 8, 422 (2012)

    2012

  23. [33]

    Lan and Y

    G. Lan and Y. Tu, Journal of The Royal Society Interface 10, 20130489 (2013)

    2013

  24. [34]

    Sartori and Y

    P. Sartori and Y. Tu, Phys. Rev. Lett. 115, 118102 (2015)

    2015

  25. [35]

    Y. Cao, H. Wang, Q. Ouyang, and Y. Tu, Nature Physics 11, 772 (2015)

    2015

  26. [36]

    C. Fei, Y. Cao, Q. Ouyang, and Y. Tu, Nature Communications 9, 1434 (2018)

    2018

  27. [37]

    Hathcock, Q

    D. Hathcock, Q. Yu, B. A. Mello, D. N. Amin, G. L. Hazelbauer, and Y. Tu, Proceedings of the National Academy of Sciences 120, e2303115120 (2023) https://www.pnas.org/doi/pdf/10.1073/pnas.2303115120

    2023 doi

  28. [38]

    Hathcock, Q

    D. Hathcock, Q. Yu, and Y. Tu, Nature Communications 15, 8892 (2024)

    2024

  29. [39]

    Ma and R

    L. Ma and R. Ranganathan, PLOS One (2012)

    2012

  30. [40]

    Takigawa-Imamura and A

    H. Takigawa-Imamura and A. Mochizuki, Journal of bi- ological rhythms 21, 405 (2006)

    2006

  31. [41]

    Clodong, U

    S. Clodong, U. D¨ uhring, L. Kronk, A. Wilde, I. Axmann, H. Herzel, and M. Kollmann, Molecular systems biology 3, 90 (2007)

    2007

  32. [42]

    Miyoshi, Y

    F. Miyoshi, Y. Nakayama, K. Kaizu, H. Iwasaki, and M. Tomita, Journal of Biological Rhythms 22, 69 (2007)

    2007

  33. [43]

    I. M. Axmann, S. Legewie, and H. Herzel, Genome In- formatics 18, 54 (2007)

    2007

  34. [44]

    Nakajima, H

    M. Nakajima, H. Ito, and T. Kondo, FEBS letters 584, 898 (2010)

    2010

  35. [45]

    A. G. Chavan, J. A. Swan, J. Heisler, C. Sancar, D. C. Ernst, M. Fang, J. G. Palacios, R. K. Spangler, C. R. Bagshaw, S. Tripathi, et al. , Science 374, eabd4453 (2021)

    2021

  36. [46]

    M. B. Bonsall and A. E. Wright, Ecology and Evolution 2, 515 (2012), https://onlinelibrary.wiley.com/doi/pdf/10.1002/ece3.206

    2012 doi

  37. [47]

    J. J. Kreider, T. Janzen, A. Bernadou, D. El- sner, B. H. Kramer, and F. J. Weissing, Nature Communications 13, 7232 (2022)

    2022

  38. [48]

    M. L. Mott and J. M. Berger, Nature Reviews Microbi- ology 5, 343 (2007)

    2007

  39. [49]

    H. Fu, F. Xiao, and S. Jun, PRX life 1, 013011 (2023)

    2023

  40. [50]

    Y. E. Antebi, J. M. Linton, H. Klumpe, B. Bintu, M. Gong, C. Su, R. McCardell, and M. B. Elowitz, Cell 170, 1184 (2017)

    2017

  41. [51]

    C. J. Su, A. Murugan, J. M. Linton, A. Yeluri, J. Bois, H. Klumpe, M. A. Langley, Y. E. Antebi, and M. B. Elowitz, Cell systems 13, 408 (2022)

    2022

  42. [52]

    H. E. Klumpe, M. A. Langley, J. M. Linton, C. J. Su, Y. E. Antebi, and M. B. Elowitz, Cell systems 13, 388 (2022)

    2022

  43. [53]

    An altruistic resource-sh aring mechanism for synchronization: The energy-speed-accuracy tradeoff

    H. E. Klumpe, J. Garcia-Ojalvo, M. B. Elowitz, and Y. E. Antebi, Cell Systems 14, 430 (2023). A B ln(1- ln σ s 2 ln σ 2 σs 2 σs 2 slope = -2 -2 -1.5 -6 -4 -2 0 2 -2 0 2 4 -6 -4 -2 0 ln Ws At /g = 0.4 At /g = 0.6 At /g = 0.8 At /g → 0 σs 2 arXiv:2502.02242v1 [cond-mat.stat-mech...

    2023 arXiv

  44. [54]

    Reif, Fundamentals of Statistical and Thermal Physics (McGraw–Hill, 1965)

    F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw–Hill, 1965)

    1965

  45. [55]

    Zhang, Y

    D. Zhang, Y. Cao, Q. Ouyang, and Y. Tu, Nature physics 16, 95 (2020)

    2020

  46. [56]

    J. M. Horowitz and T. R. Gingrich, Nature Physics 16, 15 (2020)

    2020

  47. [57]

    S. Lee, C. Hyeon, and J. Jo, Physical Review E 98, 032119 (2018). 9 -1 0 1 2 3 4 -4 -3 -2 -1 0 ln(2(1-r )) for PI ln σ2 for ARS synchronization error ln(W0Ws) slope = -1 FIG.S2: Numerical calculation for how the synchronization error decreases with energy dissipation. In gener...

    2018

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.