- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Dissipation rates from experimental uncertainty

Aishani Ghosal and Jason R. Green*

  • *Contact author: jason.green@umb.edu
PDF

Phys. Rev. Research 7, L012078 – Published 24 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012078

Abstract

Active matter and driven systems exhibit statistical fluctuations in density and particle positions that are an indirect indicator of dissipation across length and time scales. Here, we quantitatively relate these fluctuations to a thermodynamic speed limit that constrains the rates of heat and entropy production in nonequilibrium processes. By reparametrizing the speed limit set by the Fisher information, we show how to infer these dissipation rates from directly observable or controllable quantities. This approach can use available experimental data as input and avoid the need for analytically solvable microscopic models or full time-dependent probability distributions. The heat rate we predict agrees with experimental measurements for a pulled Brownian particle and a microtubule active gel, which validates the approach and suggests potential for the design of experiments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (71)

  1. J. Gladrow, N. Fakhri, F. C. MacKintosh, C. F. Schmidt, and C. P. Broedersz, Broken detailed balance of filament dynamics in active networks, Phys. Rev. Lett. 116, 248301 (2016).
  2. C. Battle, C. P. Broedersz, N. Fakhri, V. F. Geyer, J. Howard, C. F. Schmidt, and F. C. MacKintosh, Broken detailed balance at mesoscopic scales in active biological systems, Science 352, 604 (2016).
  3. G. Duclos, R. Adkins, D. Banerjee, M. S. Peterson, M. Varghese, I. Kolvin, A. Baskaran, R. A. Pelcovits, T. R. Powers, A. Baskaran et al., Topological structure and dynamics of three-dimensional active nematics, Science 367, 1120 (2020).
  4. E. R. Kay, D. A. Leigh, and F. Zerbetto, Synthetic molecular motors and mechanical machines, Angew. Chem. Int. Ed. 46, 72 (2007).
  5. S. A. P. van Rossum, M. Tena-Solsona, J. H. van Esch, R. Eelkema, and J. Boekhoven, Dissipative out-of-equilibrium assembly of man-made supramolecular materials, Chem. Soc. Rev. 46, 5519 (2017).
  6. G. Ragazzon and L. J. Prins, Energy consumption in chemical fuel-driven self-assembly, Nat. Nanotechnol. 13, 882 (2018).
  7. K. Das, L. Gabrielli, and L. J. Prins, Chemically fueled self-assembly in biology and chemistry, Angew. Chem. Int. Ed. 60, 20120 (2021).
  8. E. Del Grosso, E. Franco, L. J. Prins, and F. Ricci, Dissipative DNA nanotechnology, Nat. Chem. 14, 600 (2022).
  9. D. Barpuzary, P. J. Hurst, J. P. Patterson, and Z. Guan, Waste-free fully electrically fueled dissipative self-assembly system, J. Am. Chem. Soc. 145, 3727 (2023).
  10. O. E. Shklyaev and A. C. Balazs, Interlinking spatial dimensions and kinetic processes in dissipative materials to create synthetic systems with lifelike functionality, Nat. Nanotechnol. 19, 146 (2024).
  11. P. J. Foster, J. Bae, B. Lemma, J. Zheng, W. Ireland, P. Chandrakar, R. Boros, Z. Dogic, D. J. Needleman, and J. J. Vlassak, Dissipation and energy propagation across scales in an active cytoskeletal material, Proc. Natl. Acad. Sci. USA 120, e2207662120 (2023).
  12. J. Bae, J. Zheng, H. Zhang, P. J. Foster, D. J. Needleman, and J. J. Vlassak, A micromachined picocalorimeter sensor for liquid samples with application to chemical reactions and biochemistry, Adv. Sci. 8, 2003415 (2021).
  13. A. Rizvi, J. T. Mulvey, B. P. Carpenter, R. Talosig, and J. P. Patterson, A close look at molecular self-assembly with the transmission electron microscope, Chem. Rev. 121, 14232 (2021).
  14. Z. G. Nicolaou and A. E. Motter, Missing links as a source of seemingly variable constants in complex reaction networks, Phys. Rev. Res. 2, 043135 (2020).
  15. T. van Leeuwen, A. S. Lubbe, P. Štacko, S. J. Wezenberg, and B. L. Feringa, Dynamic control of function by light-driven molecular motors, Nat. Rev. Chem. 1, 0096 (2017).
  16. E. Moulin, L. Faour, C. C. Carmona-Vargas, and N. Giuseppone, From molecular machines to stimuli-responsive materials, Adv. Mater. 32, 1906036 (2020).
  17. L. Zhang, Y. Qiu, W.-G. Liu, H. Chen, D. Shen, B. Song, K. Cai, H. Wu, Y. Jiao, Y. Feng et al., An electric molecular motor, Nature (London) 613, 280 (2023).
  18. L. Peliti and S. Pigolotti, Stochastic Thermodynamics (Princeton University Press, New Jersey, 2021).
  19. S. B. Nicholson, L. P. García-Pintos, A. del Campo, and J. R. Green, Time–information uncertainty relations in thermodynamics, Nat. Phys. 16, 1211 (2020).
  20. R. A. Fisher, Theory of statistical estimation, in Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge University Press, Cambridge, 1925), Vol. 22, pp. 700–725.
  21. E.-j. Kim, Information geometry, fluctuations, non-equilibrium thermodynamics, and geodesics in complex systems, Entropy 23, 1393 (2021).
  22. B. R. Frieden, Science from Fisher Information (Citeseer, Cambridge, 2004), Vol. 974.
  23. S. B. Nicholson and J. R. Green, Thermodynamic speed limits from the regression of information, arXiv:2105.01588.
  24. E. Aghion and J. R. Green, Relations between timescales of stochastic thermodynamic observables, J. Non-Equilib. Thermodyn. 48, 417 (2023).
  25. E. Aghion and J. R. Green, Thermodynamic speed limits for mechanical work, J. Phys. A: Math. Theor. 56, 05LT01 (2023).
  26. Y. Oono and M. Paniconi, Steady state thermodynamics, Prog. Theor. Phys. Suppl. 130, 29 (1998).
  27. If no work is done on or by the system, then a simpler result holds [69].
  28. S. Deffner and E. Lutz, Quantum speed limit for non-Markovian dynamics, Phys. Rev. Lett. 111, 010402 (2013).
  29. T. Fogarty, S. Deffner, T. Busch, and S. Campbell, Orthogonality catastrophe as a consequence of the quantum speed limit, Phys. Rev. Lett. 124, 110601 (2020).
  30. S. Deffner, Quantum speed limits and the maximal rate of information production, Phys. Rev. Res. 2, 013161 (2020).
  31. S. Das and J. R. Green, Speed limits on deterministic chaos and dissipation, Phys. Rev. Res. 5, L012016 (2023).
  32. S. Das and J. R. Green, Maximum speed of dissipation, Phys. Rev. E 109, L052104 (2024).
  33. N. Shiraishi, K. Funo, and K. Saito, Speed limit for classical stochastic processes, Phys. Rev. Lett. 121, 070601 (2018).
  34. S. B. Nicholson, A. del Campo, and J. R. Green, Nonequilibrium uncertainty principle from information geometry, Phys. Rev. E 98, 032106 (2018).
  35. Y. Hasegawa and T. Van Vu, Uncertainty relations in stochastic processes: An information inequality approach, Phys. Rev. E 99, 062126 (2019).
  36. G. Falasco and M. Esposito, Dissipation-time uncertainty relation, Phys. Rev. Lett. 125, 120604 (2020).
  37. A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
  38. T. R. Gingrich and J. M. Horowitz, Fundamental bounds on first passage time fluctuations for currents, Phys. Rev. Lett. 119, 170601 (2017).
  39. J. Li, J. M. Horowitz, T. R. Gingrich, and N. Fakhri, Quantifying dissipation using fluctuating currents, Nat. Commun. 10, 1666 (2019).
  40. J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020).
  41. S. K. Manikandan, D. Gupta, and S. Krishnamurthy, Inferring entropy production from short experiments, Phys. Rev. Lett. 124, 120603 (2020).
  42. S. Otsubo, S. Ito, A. Dechant, and T. Sagawa, Estimating entropy production by machine learning of short-time fluctuating currents, Phys. Rev. E 101, 062106 (2020).
  43. T. Van Vu, V. T. Vo, and Y. Hasegawa, Entropy production estimation with optimal current, Phys. Rev. E 101, 042138 (2020).
  44. A. Pal, S. Reuveni, and S. Rahav, Thermodynamic uncertainty relation for first-passage times on Markov chains, Phys. Rev. Res. 3, L032034 (2021).
  45. A. Dechant and S.-I. Sasa, Improving thermodynamic bounds using correlations, Phys. Rev. X 11, 041061 (2021).
  46. P. Pietzonka and F. Coghi, Thermodynamic cost for precision of general counting observables, Phys. Rev. E 109, 064128 (2024).
  47. J. Lyu, K. J. Ray, and J. P. Crutchfield, Learning entropy production from underdamped Langevin trajectories, Phys. Rev. E 110, 064151 (2024).
  48. D. J. Skinner and J. Dunkel, Estimating entropy production from waiting time distributions, Phys. Rev. Lett. 127, 198101 (2021).
  49. E. Nitzan, A. Ghosal, and G. Bisker, Universal bounds on entropy production inferred from observed statistics, Phys. Rev. Res. 5, 043251 (2023).
  50. J. van der Meer, B. Ertel, and U. Seifert, Thermodynamic inference in partially accessible Markov networks: A unifying perspective from transition-based waiting time distributions, Phys. Rev. X 12, 031025 (2022).
  51. I. Di Terlizzi, M. Gironella, D. Herráez-Aguilar, T. Betz, F. Monroy, M. Baiesi, and F. Ritort, Variance sum rule for entropy production, Science 383, 971 (2024).
  52. I. D. Terlizzi, M. Baiesi, and F. Ritort, Variance sum rule: Proofs and solvable models, New J. Phys. 26, 063013 (2024).
  53. P. E. Harunari, A. Dutta, M. Polettini, and E. Roldán, What to learn from a few visible transitions' statistics? Phys. Rev. X 12, 041026 (2022).
  54. K. Blom, K. Song, E. Vouga, A. Godec, and D. E. Makarov, Milestoning estimators of dissipation in systems observed at a coarse resolution, Proc. Natl. Acad. Sci. USA 121, e2318333121 (2024).
  55. L. Mandelstam and I. Tamm, The uncertainty relation between energy and time in non-relativistic quantum mechanics, in Selected Papers, edited by I. E. Tamm, B. M. Bolotovskii, V. Y. Frenkel, and R. Peierls (Springer, Berlin, Heidelberg, 1991), pp. 115–123.
  56. L. P. García-Pintos, S. B. Nicholson, J. R. Green, A. del Campo, and A. V. Gorshkov, Unifying quantum and classical speed limits on observables, Phys. Rev. X 12, 011038 (2022).
  57. Y. Jung and I. Lee, Optimal design of experiments for optimization-based model calibration using Fisher information matrix, Reliab. Eng. Syst. Safety 216, 107968 (2021).
  58. G. E. P. Box, J. Stuart Hunter, and W. G. Hunter, Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed. (Wiley, New Jersey, 2005).
  59. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012078 for additional derivations and simulation details.
  60. C.-F. Gauss, Theoria Combinationis Observationum Erroribus Minimis Obnoxiae (Henricus Dieterich, Germany, 1823).
  61. R. J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (John Wiley & Sons, New Jersey, 1993), Vol. 29.
  62. A. Imparato, L. Peliti, G. Pesce, G. Rusciano, and A. Sasso, Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments, Phys. Rev. E 76, 050101(R) (2007).
  63. F. Ritort, Single-molecule experiments in biological physics: Methods and applications, J. Phys.: Condens. Matter 18, R531 (2006).
  64. With these numerical values of radius and viscosity, the inverse friction coefficient is γ=5.30×107 mN−1s−1.
  65. T. Speck, J. Mehl, and U. Seifert, Role of external flow and frame invariance in stochastic thermodynamics, Phys. Rev. Lett. 100, 178302 (2008).
  66. In the comoving frame [70], the position is initially delta function distributed ρ(x−vt0)=δ(x−x(t0)) and eventually evolves as ρ(x−vt)=e−|x−vt|2/2σx2/2πσx2 at steady state.
  67. E. L. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed. (Springer, New York, 1998).
  68. This relationship is a generalization of Gauss's error propagation law [60, 71]. Standard propagation of error is a simple approximation of the distribution ρY(y) of Y with only the first two moments, μY and σY2: Gauss's error propagation law [60] predicts the variance σY2=σX2(∂Xf|X=μX)2 and the Taylor expansion Y=f(μX)+∂Xf|X=μX(X−μX) predicts the mean μY=f(μX). It is a special case in which the function f is linear, making the error ɛ=0 and σɛ2=0.
  69. S. Ito and A. Dechant, Stochastic time evolution, information geometry, and the Cramér-Rao bound, Phys. Rev. X 10, 021056 (2020).
  70. R. van Zon and E. G. D. Cohen, Extended heat-fluctuation theorems for a system with deterministic and stochastic forces, Phys. Rev. E 69, 056121 (2004).
  71. P. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 3rd ed. (McGraw-Hill Education, Boston, MA, 2002).

Outline

Information

Phys. Rev. Research 7, L012078– Published 24 March, 2025
  • Received 7 June 2024
  • Revised 11 December 2024
  • Accepted 30 January 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation