Beat of a current.

[en] The fluctuation relation, a milestone of modern thermodynamics, is only established when a set of fundamental currents can be measured. Here we prove that it also holds for systems with hidden transitions if observations are carried "at their own beat," that is, by stopping the experiment after a fixed number of visible transitions, rather than the elapse of an external clock time. This suggests that thermodynamic symmetries are more resistant to the loss of information when described in the space of transitions.

Disciplines :

Physics

Author, co-author :

HARUNARI, Pedro ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil

GARILLI, Alberto ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Matteo POLETTINI

POLETTINI, Matteo ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Matteo POLETTINI

External co-authors :

Language :

English

Title :

Beat of a current.

Publication date :

April 2023

Journal title :

Physical Review. E

ISSN :

2470-0045

eISSN :

2470-0053

Publisher :

American Physical Society, United States

Volume :

107

Issue :

Pages :

L042105

Peer reviewed :

Peer Reviewed verified by ORBi

Focus Area :

Physics and Materials Science

Additional URL :

https://link.aps.org/article/10.1103/PhysRevE.107.L042105

Funders :

Fonds National de la Recherche Luxembourg
European Research Council
Fundação de Amparo à Pesquisa do Estado de São Paulo

Funding text :

We thank Emanuele Penocchio for helping out with the introduction, Gianmaria Falasco for suggesting the connection of the survival matrix to large deviations, Danilo Forastiere for sharing ideas, Pedro Portugal for helping with computational resources, and Michela Bernini for the illustration in Fig. . P.E.H. thanks Massimiliano Esposito for hospitality in his group. The research was supported by the National Research Fund Luxembourg (Project CORE ThermoComp No. C17/MS/11696700), by the European Research Council, Project NanoThermo (ERC-2015-CoG Agreement No. 681456), and by Grants No. 2017/24567-0 and No. 2020/03708-8, São Paulo Research Foundation (FAPESP).

Commentary :

10 pages, 7 figures

Available on ORBilu :

since 08 January 2024

Statistics

Number of views

23 (1 by Unilu)

Number of downloads

0 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenAlex citations

WoS citations^™

See more details

publications

supporting

mentioning

contrasting

Smart Citations

Citing PublicationsSupportingMentioningContrasting

View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

Bibliography

J. Schwinger, Quantum Mechanics: Symbolism of Atomic Measurements (Springer, Berlin, Heidelberg, 2003).
M. R. Wilson, J. Solà, A. Carlone, S. M. Goldup, N. Lebrasseur, and D. A. Leigh, An autonomous chemically fuelled small-molecule motor, Nature (London) 534, 235 (2016) 0028-0836 10.1038/nature18013.
S. Amano, S. D. Fielden, and D. A. Leigh, A catalysis-driven artificial molecular pump, Nature (London) 594, 529 (2021) 0028-0836 10.1038/s41586-021-03575-3.
A. Sorrenti, J. Leira-Iglesias, A. Sato, and T. M. Hermans, Non-equilibrium steady states in supramolecular polymerization, Nat. Commun. 8, 15899 (2017) 2041-1723 10.1038/ncomms15899.
S. N. Semenov, L. J. Kraft, A. Ainla, M. Zhao, M. Baghbanzadeh, V. E. Campbell, K. Kang, J. M. Fox, and G. M. Whitesides, Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions, Nature (London) 537, 656 (2016) 0028-0836 10.1038/nature19776.
R. Mallik, B. C. Carter, S. A. Lex, S. J. King, and S. P. Gross, Cytoplasmic dynein functions as a gear in response to load, Nature (London) 427, 649 (2004) 0028-0836 10.1038/nature02293.
R. D. Vale, T. S. Reese, and M. P. Sheetz, Identification of a novel force-generating protein, kinesin, involved in microtubule-based motility, Cell 42, 39 (1985) 0092-8674 10.1016/S0092-8674(85)80099-4.
M. Nishiyama, H. Higuchi, and T. Yanagida, Chemomechanical coupling of the forward and backward steps of single kinesin molecules, Nat. Cell Biol. 4, 790 (2002) 1465-7392 10.1038/ncb857.
M. Polettini and M. Esposito, Transient fluctuation theorems for the currents and initial equilibrium ensembles, J. Stat. Mech.: Theory Exp. (2014) P10033 1742-5468 10.1088/1742-5468/2014/10/P10033.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.107.L042105 for proofs, details, and further comments, which includes Refs. [9,13,14,16,19,22,41,42].
M. F. Weber and E. Frey, Master equations and the theory of stochastic path integrals, Rep. Prog. Phys. 80, 046601 (2017) 0034-4885 10.1088/1361-6633/aa5ae2.
R. Zia and B. Schmittmann, Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states, J. Stat. Mech.: Theory Exp. (2007) P07012 1742-5468 10.1088/1742-5468/2007/07/P07012.
K. Sekimoto, Derivation of the first passage time distribution for Markovian process on discrete network, arXiv:2110.02216.
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) 2160-3308 10.1103/PhysRevX.12.041026.
I. A. Martínez, G. Bisker, J. M. Horowitz, and J. M. Parrondo, Inferring broken detailed balance in the absence of observable currents, Nat. Commun. 10, 3542 (2019) 10.1038/s41467-019-11051-w.
K. Suzumura, Perron-Frobenius theorem on non-negative square matrices: An elementary proof, Hitotsubashi J. Econ. 24, 137 (1983).
S. Bo and A. Celani, Multiple-scale stochastic processes: Decimation, averaging and beyond, Phys. Rep. 670, 1 (2017) 0370-1573 10.1016/j.physrep.2016.12.003.
M. Esposito, Stochastic thermodynamics under coarse graining, Phys. Rev. E 85, 041125 (2012) 1539-3755 10.1103/PhysRevE.85.041125.
M. Polettini and M. Esposito, Effective fluctuation and response theory, J. Stat. Phys. 176, 94 (2019) 0022-4715 10.1007/s10955-019-02291-7.
M. Polettini and I. Neri, Phenomenological Boltzmann formula for currents, arXiv:2208.02888.
I. Neri and M. Polettini, Extreme value statistics of edge currents in Markov jump processes, arXiv:2208.02839.
D. Andrieux and P. Gaspard, Fluctuation theorem for currents and Schnakenberg network theory, J. Stat. Phys. 127, 107 (2007) 0022-4715 10.1007/s10955-006-9233-5.
J. Kiukas, M. Guţǎ, I. Lesanovsky, and J. P. Garrahan, Equivalence of matrix product ensembles of trajectories in open quantum systems, Phys. Rev. E 92, 012132 (2015) 1539-3755 10.1103/PhysRevE.92.012132.
A. A. Budini, R. M. Turner, and J. P. Garrahan, Fluctuating observation time ensembles in the thermodynamics of trajectories, J. Stat. Mech.: Theory Exp. (2014) P03012 1742-5468 10.1088/1742-5468/2014/03/P03012.
F. Mori, G. Gradenigo, and S. N. Majumdar, First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension, J. Stat. Mech.: Theory Exp. (2021) 103208 1742-5468 10.1088/1742-5468/ac2899.
G. Gradenigo and S. N. Majumdar, A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle, J. Stat. Mech.: Theory Exp. (2019) 053206 1742-5468 10.1088/1742-5468/ab11be.
F. Mori, P. Le Doussal, S. N. Majumdar, and G. Schehr, Condensation transition in the late-time position of a run-and-tumble particle, Phys. Rev. E 103, 062134 (2021) 2470-0045 10.1103/PhysRevE.103.062134.
S. Pigolotti, I. Neri, É. Roldán, and F. Jülicher, Generic Properties of Stochastic Entropy Production, Phys. Rev. Lett. 119, 140604 (2017) 0031-9007 10.1103/PhysRevLett.119.140604.
P. Pietzonka, Classical Pendulum Clocks Break the Thermodynamic Uncertainty Relation, Phys. Rev. Lett. 128, 130606 (2022) 0031-9007 10.1103/PhysRevLett.128.130606.
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) 2160-3308 10.1103/PhysRevX.12.031025.
D. Hartich and A. Godec, Emergent Memory and Kinetic Hysteresis in Strongly Driven Networks, Phys. Rev. X 11, 041047 (2021) 2160-3308 10.1103/PhysRevX.11.041047.
D. Hartich and A. Godec, Comment on "Inferring broken detailed balance in the absence of observable currents", arXiv:2112.08978.
G. Bisker, I. A. Martinez, J. M. Horowitz, and J. M. Parrondo, Comment on "Inferring broken detailed balance in the absence of observable currents", arXiv:2202.02064.
A. C. Barato and U. Seifert, Thermodynamic Uncertainty Relation for Biomolecular Processes, Phys. Rev. Lett. 114, 158101 (2015) 0031-9007 10.1103/PhysRevLett.114.158101.
T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Dissipation Bounds All Steady-State Current Fluctuations, Phys. Rev. Lett. 116, 120601 (2016) 0031-9007 10.1103/PhysRevLett.116.120601.
Y. Hasegawa and T. Van Vu, Fluctuation Theorem Uncertainty Relation, Phys. Rev. Lett. 123, 110602 (2019) 0031-9007 10.1103/PhysRevLett.123.110602.
É. Roldán, I. Neri, R. Chetrite, S. Gupta, S. Pigolotti, F. Jülicher, and K. Sekimoto, Martingales for physicists, arXiv:2210.09983.
V. Blickle and C. Bechinger, Realization of a micrometre-sized stochastic heat engine, Nat. Phys. 8, 143 (2012) 1745-2473 10.1038/nphys2163.
O.-P. Saira, Y. Yoon, T. Tanttu, M. Möttönen, D. V. Averin, and J. P. Pekola, Test of the Jarzynski and Crooks Fluctuation Relations in an Electronic System, Phys. Rev. Lett. 109, 180601 (2012) 0031-9007 10.1103/PhysRevLett.109.180601.
The affinity can be measured as the slope of (Equation presented) when (Equation presented) satisfies a fluctuation relation; the same holds for the effective affinity between two hidden states.
D. Andrieux and P. Gaspard, Fluctuation theorem and Onsager reciprocity relations, J. Chem. Phys. 121, 6167 (2004) 0021-9606 10.1063/1.1782391.
H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478, 1 (2009) 0370-1573 10.1016/j.physrep.2009.05.002.