{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:35:40Z","timestamp":1760240140064,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T00:00:00Z","timestamp":1553212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2010-0006733","NRF-2012R1A1A2042932","NRF-2016R1D1A1B02011106"],"award-info":[{"award-number":["NRF-2010-0006733","NRF-2012R1A1A2042932","NRF-2016R1D1A1B02011106"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002643","name":"Kwangwoon University","doi-asserted-by":"publisher","award":["Kwangwoon University Research Grant in 2016"],"award-info":[{"award-number":["Kwangwoon University Research Grant in 2016"]}],"id":[{"id":"10.13039\/501100002643","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Sagawa and Ueda established a fluctuation theorem of information exchange by revealing the role of correlations in stochastic thermodynamics and unified the non-equilibrium thermodynamics of measurement and feedback control. They considered a process where a non-equilibrium system exchanges information with other degrees of freedom such as an observer or a feedback controller. They proved the fluctuation theorem of information exchange under the assumption that the state of the other degrees of freedom that exchange information with the system does not change over time while the states of the system evolve in time. Here we relax this constraint and prove that the same form of the fluctuation theorem holds even if both subsystems co-evolve during information exchange processes. This result may extend the applicability of the fluctuation theorem of information exchange to a broader class of non-equilibrium processes, such as a dynamic coupling in biological systems, where subsystems that exchange information interact with each other.<\/jats:p>","DOI":"10.3390\/sym11030433","type":"journal-article","created":{"date-parts":[[2019,3,25]],"date-time":"2019-03-25T06:56:52Z","timestamp":1553497012000},"page":"433","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fluctuation Theorem of Information Exchange between Subsystems that Co-Evolve in Time"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8932-5415","authenticated-orcid":false,"given":"Lee","family":"Jinwoo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 01897, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"C47","DOI":"10.1038\/35011540","article-title":"From molecular to modular cell biology","volume":"402","author":"Hartwell","year":"1999","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1002\/cplx.20180","article-title":"Life, information, entropy, and time: Vehicles for semantic inheritance","volume":"13","author":"Crofts","year":"2007","journal-title":"Complexity"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1126\/science.1204553","article-title":"Information transduction capacity of noisy biochemical signaling networks","volume":"334","author":"Cheong","year":"2011","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"028101","DOI":"10.1103\/PhysRevLett.118.028101","article-title":"Biochemical Machines for the Interconversion of Mutual Information and Work","volume":"118","author":"McGrath","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","first-page":"021004","article-title":"Thermodynamics of Computational Copying in Biochemical Systems","volume":"7","author":"Ouldridge","year":"2017","journal-title":"Phys. Rev. X"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"258103","DOI":"10.1103\/PhysRevLett.115.258103","article-title":"Optimal Prediction by Cellular Signaling Networks","volume":"115","author":"Becker","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cheng, F., Liu, C., Shen, B., and Zhao, Z. (2016). Investigating cellular network heterogeneity and modularity in cancer: A network entropy and unbalanced motif approach. BMC Syst. Biol., 10.","DOI":"10.1186\/s12918-016-0309-9"},{"key":"ref_8","first-page":"e54","article-title":"SLICE: Determining cell differentiation and lineage based on single cell entropy","volume":"45","author":"Whitsett","year":"2016","journal-title":"Nucleic Acids Res."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"(2018). Statistical Dynamics of Spatial-Order Formation by Communicating Cells. iScience, 2, 27\u201340.","DOI":"10.1016\/j.isci.2018.03.013"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.cels.2015.10.012","article-title":"Molecular-Level Tuning of Cellular Autonomy Controls the Collective Behaviors of Cell Populations","volume":"1","author":"Maire","year":"2015","journal-title":"Cell Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17978","DOI":"10.1073\/pnas.1207814109","article-title":"Energetic costs of cellular computation","volume":"109","author":"Mehta","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"258102","DOI":"10.1103\/PhysRevLett.113.258102","article-title":"Energy dissipation and noise correlations in biochemical sensing","volume":"113","author":"Govern","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","unstructured":"Leff, H.S., and Rex, A.F. (2014). Maxwell\u2019s Demon: Entropy, Information, Computing, Princeton University Press."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1063\/1.881299","article-title":"Information is physical","volume":"44","author":"Landauer","year":"1991","journal-title":"Phys. Today"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1002\/bs.3830090402","article-title":"On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings","volume":"9","author":"Szilard","year":"1964","journal-title":"Behav. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"180602","DOI":"10.1103\/PhysRevLett.109.180602","article-title":"Fluctuation theorem with information exchange: Role of correlations in stochastic thermodynamics","volume":"109","author":"Sagawa","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","unstructured":"Cover, T.M., and Thomas, J.A. (2012). Elements of Information Theory, John Wiley & Sons."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Tsai, C.J., and Nussinov, R. (2014). A unified view of how allostery works?. PLoS Comput. Biol., 10.","DOI":"10.1371\/journal.pcbi.1003394"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5758","DOI":"10.1021\/acs.jctc.6b00841","article-title":"The allostery landscape: Quantifying thermodynamic couplings in biomolecular systems","volume":"12","author":"Cuendet","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1146\/annurev-conmatphys-062910-140506","article-title":"Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale","volume":"2","author":"Jarzynski","year":"2011","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"126001","DOI":"10.1088\/0034-4885\/75\/12\/126001","article-title":"Stochastic thermodynamics, fluctuation theorems and molecular machines","volume":"75","author":"Seifert","year":"2012","journal-title":"Rep. Prog. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Spinney, R., and Ford, I. (2013). Fluctuation Relations: A Pedagogical Overview. Nonequilibrium Statistical Physics of Small Systems, Wiley-VCH Verlag GmbH & Co. KGaA.","DOI":"10.1002\/9783527658701.ch1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2721","DOI":"10.1103\/PhysRevE.60.2721","article-title":"Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences","volume":"60","author":"Crooks","year":"1999","journal-title":"Phys. Rev. E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"040602","DOI":"10.1103\/PhysRevLett.95.040602","article-title":"Entropy production along a stochastic trajectory and an integral fluctuation theorem","volume":"95","author":"Seifert","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"031129","DOI":"10.1103\/PhysRevE.82.031129","article-title":"Generalized detailed fluctuation theorem under nonequilibrium feedback control","volume":"82","author":"Ponmurugan","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"061120","DOI":"10.1103\/PhysRevE.82.061120","article-title":"Nonequilibrium detailed fluctuation theorem for repeated discrete feedback","volume":"82","author":"Horowitz","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3719","DOI":"10.1088\/0305-4470\/31\/16\/003","article-title":"Fluctuation theorem for stochastic dynamics","volume":"31","author":"Kurchan","year":"1998","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1023\/A:1004541830999","article-title":"The fluctuation theorem as a Gibbs property","volume":"95","author":"Maes","year":"1999","journal-title":"J. Stat. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1023\/A:1018670721277","article-title":"Hamiltonian derivation of a detailed fluctuation theorem","volume":"98","author":"Jarzynski","year":"2000","journal-title":"J. Stat. Phys."},{"key":"ref_30","unstructured":"Goldstein, H., Poole, C., and Safko, J.L. (2001). Classical Mechanics, Pearson. [3rd ed.]."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nphys3230","article-title":"Thermodynamics of information","volume":"11","author":"Parrondo","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"080602","DOI":"10.1103\/PhysRevLett.98.080602","article-title":"Dissipation: The phase-space perspective","volume":"98","author":"Kawai","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"(2010). Generalization of the second law for a transition between nonequilibrium states. Phys. Lett. A, 375, 88\u201392.","DOI":"10.1016\/j.physleta.2010.11.002"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"(2010). Generalization of the second law for a nonequilibrium initial state. Phys. Lett. A, 374, 1001\u20131004.","DOI":"10.1016\/j.physleta.2009.12.042"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"40004","DOI":"10.1209\/0295-5075\/95\/40004","article-title":"Second law and Landauer principle far from equilibrium","volume":"95","author":"Esposito","year":"2011","journal-title":"Europhys. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"090602","DOI":"10.1103\/PhysRevLett.104.090602","article-title":"Generalized Jarzynski equality under nonequilibrium feedback control","volume":"104","author":"Sagawa","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"10005","DOI":"10.1209\/0295-5075\/95\/10005","article-title":"Thermodynamic reversibility in feedback processes","volume":"95","author":"Horowitz","year":"2011","journal-title":"Europhys. Lett."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/433\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:40:08Z","timestamp":1760186408000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/433"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,22]]},"references-count":37,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["sym11030433"],"URL":"https:\/\/doi.org\/10.3390\/sym11030433","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,3,22]]}}}