- 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

Geometric decomposition of entropy production in out-of-equilibrium systems

Andreas Dechant1, Shin-ichi Sasa1, and Sosuke Ito2,3,4

  • 1Department of Physics No. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
  • 2Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
  • 3Universal Biology Institute, The University of Tokyo, Tokyo 113-0033, Japan
  • 4JST, PRESTO, Saitama 332-0012, Japan

PDF

Phys. Rev. Research 4, L012034 – Published 18 March, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L012034

Abstract

Two qualitatively different ways of driving a physical system out of equilibrium, i.e., time-dependent and nonconservative forcing, are reflected by the decomposition of the system's entropy production into excess and housekeeping parts. We show that the difference between these two types of driving gives rise to a geometric formulation in terms of two orthogonal contributions to the currents in the system. This geometric picture in a natural way leads to variational expressions for both the excess and housekeeping entropy, which allow calculating both contributions independently from the trajectory data of the system. We demonstrate this by calculating the excess and housekeeping entropy of a particle in a time-dependent, tilted periodic potential.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (32)

  1. R. Landauer, dQ=TdS far from equilibrium, Phys. Rev. A 18, 255 (1978).
  2. Y. Oono and M. Paniconi, Steady state thermodynamics, Prog. Theor. Phys. Suppl. 130, 29 (1998).
  3. T. Hatano and S.-i. Sasa, Steady-State Thermodynamics of Langevin Systems, Phys. Rev. Lett. 86, 3463 (2001).
  4. D. P. Ruelle, Extending the definition of entropy to nonequilibrium steady states, Proc. Natl. Acad. Sci. 100, 3054 (2003).
  5. T. S. Komatsu, N. Nakagawa, S.-i. Sasa, and H. Tasaki, Steady-State Thermodynamics for Heat Conduction: Microscopic Derivation, Phys. Rev. Lett. 100, 230602 (2008).
  6. L. Bertini, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Clausius Inequality and Optimality of Quasistatic Transformations for Nonequilibrium Stationary States, Phys. Rev. Lett. 110, 020601 (2013).
  7. C. Maes and K. Netočnỳ, A nonequilibrium extension of the Clausius heat theorem, J. Stat. Phys. 154, 188 (2014).
  8. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L012034 which contains additio- nal technical details.
  9. A. Dechant, S. i. Sasa, and S. Ito, Geometric decomposition of entropy production into excess, housekeeping and coupling parts, arXiv:2202.04331.
  10. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numer. Math. 84, 375 (2000).
  11. E. Aurell, C. Mejía-Monasterio, and P. Muratore-Ginanneschi, Optimal Protocols and Optimal Transport in Stochastic Thermodynamics, Phys. Rev. Lett. 106, 250601 (2011).
  12. E. Aurell, K. Gawedzki, C. Mejía-Monasterio, R. Mohayaee, and P. Muratore-Ginanneschi, Refined second law of thermodynamics for fast random processes, J. Stat. Phys. 147, 487 (2012).
  13. A. Dechant and Y. Sakurai, Thermodynamic interpretation of Wasserstein distance, arXiv:1912.08405.
  14. C. Villani, Optimal Transport: Old and New, Grundlehren der Mathematischen Wissenschaften (Springer, Berlin, 2008).
  15. M. Nakazato and S. Ito, Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance, Phys. Rev. Research 3, 043093 (2021).
  16. S. K. Manikandan, D. Gupta, and S. Krishnamurthy, Inferring Entropy Production from Short Experiments, Phys. Rev. Lett. 124, 120603 (2020).
  17. 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).
  18. T. Van Vu, V. T. Vo, and Y. Hasegawa, Entropy production estimation with optimal current, Phys. Rev. E 101, 042138 (2020).
  19. J. Li, J. M. Horowitz, T. R. Gingrich, and N. Fakhri, Quantifying dissipation using fluctuating currents, Nat. Commun. 10, 1666 (2019).
  20. T. Speck and U. Seifert, The Jarzynski relation, fluctuation theorems, and stochastic thermodynamics for non-Markovian processes, J. Stat. Mech.: Theory Expt. (2007) L09002.
  21. M. Evstigneev, O. Zvyagolskaya, S. Bleil, R. Eichhorn, C. Bechinger, and P. Reimann, Diffusion of colloidal particles in a tilted periodic potential: Theory versus experiment, Phys. Rev. E 77, 041107 (2008).
  22. K. Sekimoto, Stochastic Energetics, Lecture Notes in Physics (Springer, Berlin, 2010).
  23. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  24. C. Maes and K. Netočnỳ, Minimum entropy production principle from a dynamical fluctuation law, J. Math. Phys. 48, 053306 (2007).
  25. T. Van Vu and Y. Hasegawa, Geometrical Bounds of the Irreversibility in Markovian Systems, Phys. Rev. Lett. 126, 010601 (2021).
  26. A. Dechant, Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes, J. Phys. A: Math. Theor. 55, 094001 (2022).
  27. V. I. Arnol'd, Mathematical Methods of Classical Mechanics, Vol. 60 (Springer Science & Business Media, New York, 2013).
  28. S. Ito, M. Oizumi, and S.-i. Amari, Unified framework for the entropy production and the stochastic interaction based on information geometry, Phys. Rev. Research 2, 033048 (2020).
  29. S.-i. Amari, Information Geometry and its Applications, Vol. 194 (Springer, New York, 2016).
  30. E. T. Jaynes, On the rationale of maximum-entropy methods, Proc. IEEE 70, 939 (1982).
  31. M. Pavon and A. Ferrante, On the geometry of maximum entropy problems, SIAM Rev. 55, 415 (2013).
  32. E. T. Jaynes, The minimum entropy production principle, Annu. Rev. Phys. Chem. 31, 579 (1980).

Outline

Information

Phys. Rev. Research 4, L012034– Published 18 March, 2022
  • Received 26 September 2021
  • Accepted 16 February 2022
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