{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T01:54:02Z","timestamp":1792115642316,"version":"4.4.0"},"reference-count":71,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Qatar National Research Fund","award":["13S-0205-200258"],"award-info":[{"award-number":["13S-0205-200258"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems.<\/jats:p>","DOI":"10.3390\/e25010165","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T02:04:45Z","timestamp":1673834685000},"page":"165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fluctuation Theorem for Information Thermodynamics of Quantum Correlated Systems"],"prefix":"10.3390","volume":"25","author":[{"given":"Jung Jun","family":"Park","sequence":"first","affiliation":[{"name":"School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyunchul","family":"Nha","sequence":"additional","affiliation":[{"name":"School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea"},{"name":"Department of Physics, Texas A&M University at Qatar, Education City, Doha 23874, Qatar"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,13]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"143001","DOI":"10.1088\/1751-8113\/49\/14\/143001","article-title":"The role of quantum information in thermodynamics\u2014A topical review","volume":"49","author":"Goold","year":"2016","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"041002","DOI":"10.1103\/RevModPhys.92.041002","article-title":"Colloquium: Statistical mechanics and thermodynamics at strong coupling: Quantum and classical","volume":"92","author":"Talkner","year":"2020","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gemmer, J., Michel, M., and Mahler, G. (2009). Quantum Thermodynamics, Springer.","DOI":"10.1007\/978-3-540-70510-9"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2401","DOI":"10.1103\/PhysRevLett.71.2401","article-title":"Probability of second law violations in shearing steady states","volume":"71","author":"Evans","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2694","DOI":"10.1103\/PhysRevLett.74.2694","article-title":"Dynamical Ensembles in Nonequilibrium Statistical Mechanics","volume":"74","author":"Gallavotti","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1103\/PhysRevLett.78.2690","article-title":"Nonequilibrium Equality for Free Energy Differences","volume":"78","author":"Jarzynski","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","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_9","unstructured":"Tasaki, H. (2000). Jarzynski Relations for Quantum Systems and Some Applications. arXiv."},{"key":"ref_10","unstructured":"Kurchan, J. (2000). A Quantum Fluctuation Theorem. arXiv."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"F569","DOI":"10.1088\/1751-8113\/40\/26\/F08","article-title":"The Tasaki\u2013Crooks quantum fluctuation theorem","volume":"40","author":"Talkner","year":"2007","journal-title":"J. Phys. Math. Theor."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"P10023","DOI":"10.1088\/1742-5468\/2008\/10\/P10023","article-title":"On the Jarzynski relation for dissipative quantum dynamics","volume":"2008","author":"Crooks","year":"2008","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1103\/RevModPhys.81.1665","article-title":"Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems","volume":"81","author":"Esposito","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"210401","DOI":"10.1103\/PhysRevLett.102.210401","article-title":"Fluctuation Theorem for Arbitrary Open Quantum Systems","volume":"102","author":"Campisi","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"140601","DOI":"10.1103\/PhysRevLett.105.140601","article-title":"Fluctuation Theorems for Continuously Monitored Quantum Fluxes","volume":"105","author":"Campisi","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1103\/RevModPhys.83.771","article-title":"Colloquium: Quantum fluctuation relations: Foundations and applications","volume":"83","author":"Campisi","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"272001","DOI":"10.1088\/1751-8113\/45\/27\/272001","article-title":"An information-theoretic equality implying the Jarzynski relation","volume":"45","author":"Vedral","year":"2012","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_19","first-page":"011019","article-title":"Fully Quantum Fluctuation Theorems","volume":"8","author":"Aberg","year":"2018","journal-title":"Phys. Rev. X"},{"key":"ref_20","first-page":"041017","article-title":"Fluctuating Work: From Quantum Thermodynamical Identities to a Second Law Equality","volume":"6","author":"Alhambra","year":"2016","journal-title":"Phys. Rev. X"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"032137","DOI":"10.1103\/PhysRevE.90.032137","article-title":"Nonequilibrium quantum fluctuations of work","volume":"90","author":"Allahverdyan","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"022131","DOI":"10.1103\/PhysRevE.93.022131","article-title":"Aspects of quantum work","volume":"93","author":"Talkner","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"043013","DOI":"10.1088\/1367-2630\/aa62ba","article-title":"Entropic equality for worst-case work at any protocol speed","volume":"19","author":"Dahlsten","year":"2017","journal-title":"New J. Phys."},{"key":"ref_24","unstructured":"Quan, H., and Dong, H. (2008). Quantum Crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir. arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"012131","DOI":"10.1103\/PhysRevE.92.012131","article-title":"Jarzynski equality, Crooks fluctuation theorem, and the fluctuation theorems of heat for arbitrary initial states","volume":"92","author":"Gong","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1007\/s10955-012-0557-z","article-title":"Quantum Fluctuation Relations for the Lindblad Master Equation","volume":"148","author":"Chetrite","year":"2012","journal-title":"J. Stat. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"034101","DOI":"10.1103\/PhysRevA.77.034101","article-title":"Quantum operation time reversal","volume":"77","author":"Crooks","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_28","first-page":"031029","article-title":"Fluctuation Theorems for a Quantum Channel","volume":"9","author":"Kwon","year":"2019","journal-title":"Phys. Rev. X"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"124","DOI":"10.22331\/q-2019-02-25-124","article-title":"Coherent fluctuation relations: From the abstract to the concrete","volume":"3","author":"Holmes","year":"2019","journal-title":"Quantum"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6383","DOI":"10.1038\/ncomms7383","article-title":"Description of quantum coherence in thermodynamic processes requires constraints beyond free energy","volume":"6","author":"Lostaglio","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"414007","DOI":"10.1088\/1751-8121\/aac115","article-title":"Quantum coherence fluctuation relations","volume":"51","author":"Morris","year":"2018","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"032129","DOI":"10.1103\/PhysRevE.92.032129","article-title":"Nonequilibrium potential and fluctuation theorems for quantum maps","volume":"92","author":"Manzano","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"013013","DOI":"10.1088\/1367-2630\/12\/1\/013013","article-title":"Entropy production as correlation between system and reservoir","volume":"12","author":"Esposito","year":"2010","journal-title":"New J. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"030601","DOI":"10.1103\/PhysRevLett.113.030601","article-title":"Experimental Observation of the Role of Mutual Information in the Nonequilibrium Dynamics of a Maxwell Demon","volume":"113","author":"Koski","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"062125","DOI":"10.1103\/PhysRevE.92.062125","article-title":"How an autonomous quantum Maxwell demon can harness correlated information","volume":"92","author":"Chapman","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_36","first-page":"041003","article-title":"Information Processing and the Second Law of Thermodynamics: An Inclusive, Hamiltonian Approach","volume":"3","author":"Deffner","year":"2013","journal-title":"Phys. Rev. X"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"P03006","DOI":"10.1088\/1742-5468\/2015\/03\/P03006","article-title":"Multipartite information flow for multiple Maxwell demons","volume":"2015","author":"Horowitz","year":"2015","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_38","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_39","first-page":"021003","article-title":"Quantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions","volume":"7","author":"Strasberg","year":"2017","journal-title":"Phys. Rev. X"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"062107","DOI":"10.1103\/PhysRevE.90.062107","article-title":"Second laws for an information driven current through a spin valve","volume":"90","author":"Strasberg","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"125007","DOI":"10.1088\/1367-2630\/16\/12\/125007","article-title":"Second-law-like inequalities with information and their interpretations","volume":"16","author":"Horowitz","year":"2014","journal-title":"New J. Phys."},{"key":"ref_42","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_43","doi-asserted-by":"crossref","first-page":"P02016","DOI":"10.1088\/1742-5468\/2014\/02\/P02016","article-title":"Stochastic thermodynamics of bipartite systems: Transfer entropy inequalities and a Maxwell\u2019s demon interpretation","volume":"2014","author":"Hartich","year":"2014","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"040601","DOI":"10.1103\/PhysRevLett.110.040601","article-title":"Thermodynamics of a Physical Model Implementing a Maxwell Demon","volume":"110","author":"Strasberg","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"030601","DOI":"10.1103\/PhysRevLett.108.030601","article-title":"Thermodynamics of Genuine Nonequilibrium States under Feedback Control","volume":"108","author":"Abreu","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"150603","DOI":"10.1103\/PhysRevLett.122.150603","article-title":"Thermodynamics of Quantum Information Flows","volume":"122","author":"Esposito","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","first-page":"031015","article-title":"Thermodynamics with Continuous Information Flow","volume":"4","author":"Horowitz","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"090601","DOI":"10.1103\/PhysRevLett.104.090601","article-title":"Three Detailed Fluctuation Theorems","volume":"104","author":"Esposito","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"090601","DOI":"10.1103\/PhysRevLett.112.090601","article-title":"Unifying Three Perspectives on Information Processing in Stochastic Thermodynamics","volume":"112","author":"Barato","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"100601","DOI":"10.1103\/PhysRevLett.119.100601","article-title":"Fluctuation Theorem for Many-Body Pure Quantum States","volume":"119","author":"Iyoda","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1007\/BF01341281","article-title":"\u00dcber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen","volume":"53","author":"Szilard","year":"1929","journal-title":"Z. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Leff, H., and Rex, A. (2002). Maxwell\u2019s Demon 2 Entropy, Classical and Quantum Information, Computing, CRC Press.","DOI":"10.1201\/9781420033991"},{"key":"ref_53","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_54","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_55","doi-asserted-by":"crossref","first-page":"052121","DOI":"10.1103\/PhysRevE.88.052121","article-title":"Integral quantum fluctuation theorems under measurement and feedback control","volume":"88","author":"Funo","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"042113","DOI":"10.1103\/PhysRevE.92.042113","article-title":"Exchange fluctuation theorem for correlated quantum systems","volume":"92","author":"Jevtic","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_57","first-page":"031037","article-title":"Quantum Fluctuation Theorems for Arbitrary Environments: Adiabatic and Nonadiabatic Entropy Production","volume":"8","author":"Manzano","year":"2018","journal-title":"Phys. Rev. X"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"052128","DOI":"10.1103\/PhysRevE.101.052128","article-title":"Information fluctuation theorem for an open quantum bipartite system","volume":"101","author":"Park","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10955-011-0153-7","article-title":"Quantum Jarzynski-Sagawa-Ueda Relations","volume":"143","author":"Morikuni","year":"2011","journal-title":"J. Stat. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"125012","DOI":"10.1088\/1367-2630\/15\/12\/125012","article-title":"Role of mutual information in entropy production under information exchanges","volume":"15","author":"Sagawa","year":"2013","journal-title":"New J. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"10011","DOI":"10.1209\/0295-5075\/117\/10011","article-title":"Information thermodynamics for a multi-feedback process with time delay","volume":"117","author":"Kwon","year":"2017","journal-title":"EPL Europhys. Lett."},{"key":"ref_62","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_63","doi-asserted-by":"crossref","first-page":"050102","DOI":"10.1103\/PhysRevE.75.050102","article-title":"Fluctuation theorems: Work is not an observable","volume":"75","author":"Talkner","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1103\/PhysRev.44.31","article-title":"Quantum Statistics of Almost Classical Assemblies","volume":"44","author":"Kirkwood","year":"1933","journal-title":"Phys. Rev."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1103\/RevModPhys.17.195","article-title":"On the Analogy Between Classical and Quantum Mechanics","volume":"17","author":"Dirac","year":"1945","journal-title":"Rev. Mod. Phys."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1103\/PhysRev.108.565","article-title":"Distribution Functions for Noncommuting Operators","volume":"108","author":"Barut","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1143\/PTP.26.722","article-title":"Correlation between Measurements in Quantum Theory","volume":"26","author":"Margenau","year":"1961","journal-title":"Prog. Theor. Phys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"080501","DOI":"10.1103\/PhysRevLett.104.080501","article-title":"Unified View of Quantum and Classical Correlations","volume":"104","author":"Modi","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/RevModPhys.84.1","article-title":"Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits","volume":"84","author":"Nation","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"075005","DOI":"10.1088\/1367-2630\/17\/7\/075005","article-title":"Quantum nonequilibrium equalities with absolute irreversibility","volume":"17","author":"Funo","year":"2015","journal-title":"New J. Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"200403","DOI":"10.1103\/PhysRevLett.129.200403","article-title":"Canonically Consistent Quantum Master Equation","volume":"129","author":"Becker","year":"2022","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/165\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:05:35Z","timestamp":1760119535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,13]]},"references-count":71,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010165"],"URL":"https:\/\/doi.org\/10.3390\/e25010165","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,13]]}}}