Papers
Topics
Authors
Recent
Search
2000 character limit reached

Thermodynamic bounds on generalized transport: From single-molecule to bulk observables

Published 29 Feb 2024 in cond-mat.stat-mech, cond-mat.soft, math-ph, math.MP, math.PR, and physics.bio-ph | (2403.00048v3)

Abstract: We prove that the transport of any differentiable scalar observable in $d$-dimensional non-equilibrium systems is bounded from above by the total entropy production scaled by the amount the observation "stretches" microscopic coordinates. The result--a time-integrated generalized speed limit--reflects the thermodynamic cost of transport of observables, and places underdamped and overdamped stochastic dynamics on equal footing with deterministic motion. Our work allows for stochastic thermodynamics to make contact with bulk experiments, and fills an important gap in thermodynamic inference, since microscopic dynamics is, at least for short times, underdamped. Requiring only averages but not sample-to-sample fluctuations, the proven transport bound is practical and applicable not only to single-molecule but also bulk experiments where only averages are observed, which we demonstrate by examples. Our results may facilitate thermodynamic inference on molecular machines without an obvious directionality from bulk observations of transients probed, e.g.\ in time-resolved X-ray scattering.

Authors (2)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (53)
  1. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  2. U. Seifert, Entropy production along a stochastic trajectory and an integral fluctuation theorem, Phys. Rev. Lett. 95, 040602 (2005).
  3. A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
  4. T. R. Gingrich, G. M. Rotskoff, and J. M. Horowitz, Inferring dissipation from current fluctuations, J. Phys. A: Math. Theor. 50, 184004 (2017).
  5. T. Van Vu and Y. Hasegawa, Uncertainty relations for underdamped langevin dynamics, Phys. Rev. E 100, 032130 (2019).
  6. J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2019).
  7. S. K. Manikandan, D. Gupta, and S. Krishnamurthy, Inferring entropy production from short experiments, Phys. Rev. Lett. 124, 120603 (2020).
  8. K. Liu, Z. Gong, and M. Ueda, Thermodynamic uncertainty relation for arbitrary initial states, Phys. Rev. Lett. 125, 140602 (2020).
  9. T. Koyuk and U. Seifert, Thermodynamic uncertainty relation for time-dependent driving, Phys. Rev. Lett. 125, 260604 (2020).
  10. C. Dieball and A. Godec, Coarse graining empirical densities and currents in continuous-space steady states, Phys. Rev. Res. 4, 033243 (2022b).
  11. A. Dechant and S.-i. Sasa, Continuous time reversal and equality in the thermodynamic uncertainty relation, Phys. Rev. Res. 3, L042012 (2021a).
  12. A. Dechant and S.-i. Sasa, Improving thermodynamic bounds using correlations, Phys. Rev. X 11, 041061 (2021b).
  13. C. Dieball and A. Godec, Direct route to thermodynamic uncertainty relations and their saturation, Phys. Rev. Lett. 130, 087101 (2023).
  14. K. Brandner, K. Saito, and U. Seifert, Strong bounds on onsager coefficients and efficiency for three-terminal thermoelectric transport in a magnetic field, Phys. Rev. Lett. 110, 070603 (2013).
  15. N. Shiraishi, K. Funo, and K. Saito, Speed limit for classical stochastic processes, Phys. Rev. Lett. 121, 070601 (2018).
  16. N. Shiraishi and K. Saito, Information-theoretical bound of the irreversibility in thermal relaxation processes, Phys. Rev. Lett. 123, 110603 (2019).
  17. G. Falasco and M. Esposito, Dissipation-time uncertainty relation, Phys. Rev. Lett. 125, 120604 (2020).
  18. K. Yoshimura and S. Ito, Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks, Phys. Rev. Lett. 127, 160601 (2021).
  19. E. Aurell, C. Mejía-Monasterio, and P. Muratore-Ginanneschi, Optimal protocols and optimal transport in stochastic thermodynamics, Phys. Rev. Lett. 106, 250601 (2011).
  20. A. Dechant and S.-i. Sasa, Entropic bounds on currents in Langevin systems, Phys. Rev. E 97, 062101 (2018).
  21. P. Pietzonka, Classical pendulum clocks break the thermodynamic uncertainty relation, Phys. Rev. Lett. 128, 130606 (2022).
  22. L. P. Fischer, H.-M. Chun, and U. Seifert, Free diffusion bounds the precision of currents in underdamped dynamics, Phys. Rev. E 102, 012120 (2020).
  23. C. Kwon and H. K. Lee, Thermodynamic uncertainty relation for underdamped dynamics driven by time-dependent protocols, New J. Phys. 24, 013029 (2022).
  24. R.-S. Fu and T. R. Gingrich, Thermodynamic uncertainty relation for Langevin dynamics by scaling time, Phys. Rev. E 106, 024128 (2022).
  25. C. Ratzke, B. Hellenkamp, and T. Hugel, Four-colour fret reveals directionality in the hsp90 multicomponent machinery, Nat. Commun. 5, 4192 (2014).
  26. D. Sato, T. Hikima, and M. Ikeguchi, Time-resolved small-angle X-ray scattering of protein cage assembly, in Protein Cages (Springer US, 2023) p. 211.
  27. J. Stamatoff, An approach for time-resolved x-ray scattering, Biophys. J. 26, 325 (1979).
  28. M. P. Leighton and D. A. Sivak, Dynamic and thermodynamic bounds for collective motor-driven transport, Phys. Rev. Lett. 129, 118102 (2022).
  29. M. P. Leighton and D. A. Sivak, Inferring subsystem efficiencies in bipartite molecular machines, Phys. Rev. Lett. 130, 178401 (2023).
  30. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numer. Math. 84, 375 (2000).
  31. A. Dechant, Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes, J. Phys. A: Math. Theor. 55, 094001 (2022).
  32. H. Risken, The Fokker-Planck Equation (Springer Berlin Heidelberg, 1989).
  33. G. Wilemski, On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion, J. Stat. Phys. 14, 153 (1976).
  34. See Supplemental Material at […].
  35. U. Seifert, Stochastic thermodynamics: From principles to the cost of precision, Physica (Amsterdam) 504A, 176 (2018).
  36. A. C. Barato and U. Seifert, Cost and precision of Brownian clocks, Phys. Rev. X 6, 041053 (2016).
  37. K. Dave and M. Gruebele, Fast-folding proteins under stress, Cell. Mol. Life. Sci. 72, 4273 (2015).
  38. J. Kubelka, Time-resolved methods in biophysics. 9. laser temperature-jump methods for investigating biomolecular dynamics, Photochem. Photobiol. Sci. 8, 499 (2009).
  39. J. K. G. Dhont, An introduction to dynamics of colloids, Studies in Interface Science (Elsevier, 1996).
  40. D. I. Svergun and M. H. J. Koch, Small-angle scattering studies of biological macromolecules in solution, Rep. Prog. Phys. 66, 1735 (2003).
  41. A. Lapolla and A. Godec, Faster uphill relaxation in thermodynamically equidistant temperature quenches, Phys. Rev. Lett. 125, 110602 (2020).
  42. C. Dieball, G. Wellecke, and A. Godec, Asymmetric thermal relaxation in driven systems: Rotations go opposite ways, Phys. Rev. Res. 5, L042030 (2023).
  43. V. Blickle and C. Bechinger, Realization of a micrometre-sized stochastic heat engine, Nat. Phys. 8, 143 (2011).
  44. Alternatively we can also derive a bound for Δ⁢StotΔsubscript𝑆tot\Delta S_{\rm tot}roman_Δ italic_S start_POSTSUBSCRIPT roman_tot end_POSTSUBSCRIPT but we opt for Δ⁢(T⁢Stot)Δ𝑇subscript𝑆tot\Delta(TS_{\rm tot})roman_Δ ( italic_T italic_S start_POSTSUBSCRIPT roman_tot end_POSTSUBSCRIPT ) for a “direct” energetic interpretation.
  45. More precisely, a given γ⁢[Tp⁢(t)−Tp⁢(0)]2/κ𝛾superscriptdelimited-[]subscript𝑇p𝑡subscript𝑇p02𝜅\gamma[T_{\rm p}(t)-T_{\rm p}(0)]^{2}/\kappaitalic_γ [ italic_T start_POSTSUBSCRIPT roman_p end_POSTSUBSCRIPT ( italic_t ) - italic_T start_POSTSUBSCRIPT roman_p end_POSTSUBSCRIPT ( 0 ) ] start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / italic_κ.
  46. A. Dechant, N. Kiesel, and E. Lutz, Underdamped stochastic heat engine at maximum efficiency, EPL (Europhysics Letters) 119, 50003 (2017).
  47. A. Dechant, J. Garnier-Brun, and S.-i. Sasa, Thermodynamic bounds on correlation times, Phys. Rev. Lett. 131, 167101 (2023).
  48. H. Risken, The Fokker-Planck Equation. Springer Berlin Heidelberg, Sept., 1989.
  49. C. Dieball and A. Godec, “Direct route to thermodynamic uncertainty relations and their saturation,” Phys. Rev. Lett. 130 (2023) 087101.
  50. C. Dieball, G. Wellecke, and A. Godec, “Asymmetric thermal relaxation in driven systems: Rotations go opposite ways,” Phys. Rev. Res. 5 (2023) L042030.
  51. C. Dieball, D. Krapf, M. Weiss, and A. Godec, “Scattering fingerprints of two-state dynamics,” New J. Phys. 24 (2022) 023004.
  52. A. Lapolla and A. Godec, “Faster uphill relaxation in thermodynamically equidistant temperature quenches,” Phys. Rev. Lett. 125 (2020) 110602.
  53. A. Dechant, J. Garnier-Brun, and S.-i. Sasa, “Thermodynamic bounds on correlation times,” Phys. Rev. Lett. 131 (2023) 167101.
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 3 tweets with 6 likes about this paper.

Sign Up for Free