{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T00:47:57Z","timestamp":1770598077024,"version":"3.49.0"},"reference-count":87,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p>Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modelling. In this paper, we turn to the famous Schr\u00f6dinger\u2019s book \u201cWhat is life?\u201d and reformulate his speculations in terms of this theory. Schr\u00f6dinger pointed to order preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schr\u00f6dinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preserve the order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment [Formula: see text]: 1) entropy (disorder) increasing in the process of adaptation to the specific features of [Formula: see text]; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.<\/jats:p>","DOI":"10.1142\/s1230161222500160","type":"journal-article","created":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T03:26:24Z","timestamp":1675308384000},"source":"Crossref","is-referenced-by-count":8,"title":["\u201cWhat Is Life?\u201d: Open Quantum Systems Approach"],"prefix":"10.1142","volume":"29","author":[{"given":"Irina","family":"Basieva","sequence":"first","affiliation":[{"name":"Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences, V\u00e4xj\u00f6, SE\u2013351 95, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei","family":"Khrennikov","sequence":"additional","affiliation":[{"name":"Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences, V\u00e4xj\u00f6, SE\u2013351 95, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,2,1]]},"reference":[{"key":"S1230161222500160BIB001","volume-title":"What is life?","author":"Schr\u00f6dinger E.","year":"1944"},{"key":"S1230161222500160BIB002","volume-title":"Quantum information. An overview","author":"Jaeger G.","year":"2007"},{"key":"S1230161222500160BIB003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139525343"},{"key":"S1230161222500160BIB004","volume-title":"Quantum theory from first principles (An informational approach)","author":"D\u2019Ariano G. M.","year":"2019"},{"issue":"4","key":"S1230161222500160BIB005","first-page":"313","volume":"9","author":"Ingarden R. S.","year":"1961","journal-title":"S\u00e9r. Sci. Math. Astronom. Phys."},{"issue":"10","key":"S1230161222500160BIB006","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1002\/prop.19640121002","volume":"12","author":"Ingarden R. S.","year":"1964","journal-title":"Fortschritte der Physik"},{"issue":"12","key":"S1230161222500160BIB007","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1002\/prop.19650131202","volume":"13","author":"Ingarden R. S.","year":"1965","journal-title":"Fortschritte der Physik"},{"issue":"1","key":"S1230161222500160BIB008","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4064\/cm-9-1-131-150","volume":"9","author":"Ingarden R. S.","year":"1962","journal-title":"Colloquium Mathematicum"},{"key":"S1230161222500160BIB009","first-page":"209","volume":"11","author":"Ingarden R. S.","year":"1963","journal-title":"S\u00e9r. Sci. Math. Astronom. Phys."},{"issue":"1","key":"S1230161222500160BIB010","first-page":"61","volume":"16","author":"Ingarden R. S.","year":"1968","journal-title":"S\u00e9r. Sci. Math. Astronom. Phys."},{"key":"S1230161222500160BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1882-0"},{"key":"S1230161222500160BIB012","volume-title":"Irreversible quantum dynamics","author":"Benatti F.","year":"2010"},{"issue":"2","key":"S1230161222500160BIB013","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/s11538-006-9141-5","volume":"69","author":"Gatenby R. A.","year":"2007","journal-title":"Bull. Math. Biology"},{"key":"S1230161222500160BIB014","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1126\/science.168.3939.1545","volume":"168","author":"Johnson H. A.","year":"1970","journal-title":"Science"},{"key":"S1230161222500160BIB015","first-page":"354","volume-title":"Complexity, Entropy, and the Physics of Information","author":"Wheeler J. A.","year":"1990"},{"key":"S1230161222500160BIB016","volume-title":"Quantum theory: Reconsideration of foundations","author":"Khrennikov A.","year":"2002"},{"key":"S1230161222500160BIB017","series-title":"AIP Conf. Proceedings","volume-title":"Quantum theory: Reconsideration of foundations \u2013 3","volume":"810","author":"Adenier G.","year":"2006"},{"key":"S1230161222500160BIB018","volume-title":"Quantum theory: reconsideration of foundations \u2013 2","author":"Khrennikov A.","year":"2004"},{"key":"S1230161222500160BIB019","series-title":"AIP Conf. Proceedings","volume-title":"Foundations of probability and physics \u2013 6","volume":"1424","author":"D\u2019Ariano G. M.","year":"2012"},{"key":"S1230161222500160BIB020","first-page":"463","volume-title":"Quantum theory: Reconsideration of foundations","author":"Fuchs C. A.","year":"2002"},{"key":"S1230161222500160BIB021","volume-title":"Epistemology and probability: Bohr, Heisenberg, Schr\u00f6dinger and the nature of quantum-theoretical thinking","author":"Plotnitsky A.","year":"2009"},{"key":"S1230161222500160BIB022","doi-asserted-by":"crossref","first-page":"062348","DOI":"10.1103\/PhysRevA.81.062348","volume":"81","author":"Chiribella G.","year":"2020","journal-title":"Phys. Rev. A"},{"key":"S1230161222500160BIB023","series-title":"AIP Conf. Proceedings","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1063\/1.3688980","volume-title":"Foundations of probability and physics \u2013 6","volume":"1424","author":"Chiribella G.","year":"2012"},{"key":"S1230161222500160BIB024","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-9819-8","volume-title":"Quantum Adaptivity in biology: from genetics to cognition","author":"Asano M.","year":"2015"},{"key":"S1230161222500160BIB025","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1023\/A:1018885632116","volume":"29","author":"Khrennikov A.","year":"1999","journal-title":"Found. Physics"},{"key":"S1230161222500160BIB026","doi-asserted-by":"publisher","DOI":"10.1016\/S0303-2647(03)00041-8"},{"issue":"3","key":"S1230161222500160BIB027","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1023\/B:OPSY.0000047570.68941.9d","volume":"11","author":"Khrennikov A.","year":"2004","journal-title":"Open Syst. Inform. Dyn."},{"key":"S1230161222500160BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0479-3"},{"key":"S1230161222500160BIB029","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-05101-2"},{"key":"S1230161222500160BIB030","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511997716"},{"key":"S1230161222500160BIB031","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139003261"},{"key":"S1230161222500160BIB032","doi-asserted-by":"crossref","DOI":"10.1142\/q0080","volume-title":"Quantum methods in social science: A first course","author":"Haven E.","year":"2017"},{"issue":"11","key":"S1230161222500160BIB033","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1007\/s10773-005-8973-3","volume":"44","author":"Haven E.","year":"2005","journal-title":"Int. J. Theor. Phys."},{"key":"S1230161222500160BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2005.11.005"},{"key":"S1230161222500160BIB035","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2006.01.003"},{"key":"S1230161222500160BIB036","doi-asserted-by":"crossref","unstructured":"E. Pothos, and J. R. Busemeyer, Proceedings of Royal Society B 276, 2171 (2009).","DOI":"10.1098\/rspb.2009.0121"},{"key":"S1230161222500160BIB037","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2009-00245-9"},{"key":"S1230161222500160BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2011.04.022"},{"key":"S1230161222500160BIB039","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jmp.2011.12.003","volume":"56","author":"Dzhafarov E. N.","year":"2012","journal-title":"J. Math. Psych."},{"key":"S1230161222500160BIB040","doi-asserted-by":"publisher","DOI":"10.1007\/s11693-012-9091-1"},{"key":"S1230161222500160BIB041","doi-asserted-by":"crossref","unstructured":"M. Asano, I. Basieva, A. Khrennikov, M. Ohya, Y. Tanaka, and I. Yamato, Towards modeling of epigenetic evolution with the aid of theory of open quantum Systems, AIP Conf. Proceedings 1508, Melville, NY, 2012, pp. 75\u201385, https:\/\/doi.org\/10.1063\/1.4773118.","DOI":"10.1063\/1.4773118"},{"key":"S1230161222500160BIB042","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202512500534"},{"key":"S1230161222500160BIB043","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1111\/tops.12040","volume":"5","author":"Wang Z.","year":"2013","journal-title":"Top. Cogn. Sc."},{"key":"S1230161222500160BIB044","doi-asserted-by":"crossref","first-page":"9431","DOI":"10.1073\/pnas.1407756111","volume":"111","author":"Wang Z.","year":"2014","journal-title":"PNAS"},{"key":"S1230161222500160BIB045","doi-asserted-by":"crossref","first-page":"324","DOI":"10.14704\/nq.2014.12.3.750","volume":"12","author":"Khrennikov A.","year":"2014","journal-title":"NeuroQuantology"},{"key":"S1230161222500160BIB046","doi-asserted-by":"publisher","DOI":"10.1111\/tops.12065"},{"issue":"3","key":"S1230161222500160BIB047","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmp.2014.09.003","volume":"62","author":"Khrennikov A.","year":"2014","journal-title":"J. Math. Psych."},{"key":"S1230161222500160BIB048","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-54943-4_24","volume-title":"Quantum Interaction, QI 2013","volume":"8369","author":"Khrennikova P.","year":"2014"},{"key":"S1230161222500160BIB049","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/2014\/T163\/014007"},{"key":"S1230161222500160BIB050","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/2014\/T163\/014006"},{"key":"S1230161222500160BIB051","doi-asserted-by":"crossref","first-page":"e110909","DOI":"10.1371\/journal.pone.0110909","volume":"9","author":"Khrennikov A.","year":"2014","journal-title":"PLOS ONE"},{"key":"S1230161222500160BIB052","first-page":"1","volume":"10","author":"Boyer-Kassem T.","year":"2015","journal-title":"Theor. Decis."},{"key":"S1230161222500160BIB053","doi-asserted-by":"crossref","first-page":"20150099","DOI":"10.1098\/rsta.2015.0099","volume":"374","author":"Dzhafarov E. N.","year":"2015","journal-title":"Phil. Trans. Royal Soc. A"},{"key":"S1230161222500160BIB054","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-015-9929-y"},{"key":"S1230161222500160BIB055","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-015-9932-3"},{"key":"S1230161222500160BIB056","first-page":"997","volume":"6","author":"Khrennikov A.","year":"2015","journal-title":"Frontiers Psych."},{"key":"S1230161222500160BIB057","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2015.0245"},{"key":"S1230161222500160BIB058","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jmp.2016.02.009","volume":"71","author":"Khrennikova P.","year":"2016","journal-title":"J. Math. Psych."},{"key":"S1230161222500160BIB059","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.pbiomolbio.2017.05.013","volume":"130","author":"Asano M.","year":"2017","journal-title":"Prog. Biophys. Molecular Biol. Part A"},{"key":"S1230161222500160BIB060","doi-asserted-by":"publisher","DOI":"10.3390\/e19030112"},{"key":"S1230161222500160BIB061","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2016.07.006"},{"key":"S1230161222500160BIB062","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2016.10.003"},{"key":"S1230161222500160BIB063","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.jmp.2016.08.005","volume":"77","author":"Basieva I.","year":"2017","journal-title":"J. Math. Psych."},{"key":"S1230161222500160BIB064","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-34531-3"},{"issue":"12","key":"S1230161222500160BIB065","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.3390\/e21121195","volume":"21","author":"Lawless W. F.","year":"2019","journal-title":"Entropy"},{"issue":"10","key":"S1230161222500160BIB066","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.3390\/e22101169","volume":"22","author":"Bagarello F.","year":"2020","journal-title":"Entropy"},{"issue":"1","key":"S1230161222500160BIB067","doi-asserted-by":"crossref","first-page":"37","DOI":"10.3390\/e22010037","volume":"22","author":"Ozawa M.","year":"2020","journal-title":"Entropy"},{"issue":"6","key":"S1230161222500160BIB068","doi-asserted-by":"crossref","first-page":"68","DOI":"10.3390\/e22060681","volume":"22","author":"Yukalov V. I.","year":"2020","journal-title":"Entropy"},{"key":"S1230161222500160BIB069","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198519737.001.0001"},{"key":"S1230161222500160BIB070","volume-title":"Advanced field theory: Micro, macro and thermal concepts","author":"Umezawa H.","year":"1993"},{"key":"S1230161222500160BIB071","first-page":"91","volume":"1","author":"Hameroff S.","year":"1994","journal-title":"J. Cons. Stud."},{"key":"S1230161222500160BIB072","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1142\/S0217979295000380","volume":"9","author":"Vitiello G.","year":"1995","journal-title":"Int. J. Mod. Phys."},{"key":"S1230161222500160BIB073","series-title":"Advances in Consciousness Research","doi-asserted-by":"crossref","DOI":"10.1075\/aicr.32","volume-title":"My double unveiled: The dissipative quantum model of brain","author":"Vitiello G.","year":"2001"},{"key":"S1230161222500160BIB074","first-page":"450","volume":"38","author":"Bell J. S.","year":"1966","journal-title":"Rev. Mod. Phys."},{"key":"S1230161222500160BIB075","first-page":"59","volume":"17","author":"Kochen S.","year":"1967","journal-title":"J. Math. Mech."},{"key":"S1230161222500160BIB076","doi-asserted-by":"crossref","unstructured":"K. Svozil, On Counterfactuals and contextuality, Foundations of probability and physics \u2013 3, AIP Conf. Proceedings 750, Melville, NY, 2005, pp. 351\u2013360.","DOI":"10.1063\/1.1874586"},{"key":"S1230161222500160BIB077","doi-asserted-by":"crossref","first-page":"04010","DOI":"10.1103\/PhysRevA.80.040102","volume":"80","author":"Svozil K.","year":"2009","journal-title":"Phys. Rev. A"},{"key":"S1230161222500160BIB078","volume-title":"Quantum logic","author":"Svozil K.","year":"1998"},{"key":"S1230161222500160BIB079","volume-title":"Mathematical foundations of quantum mechanics","author":"von Neumann J.","year":"1955"},{"key":"S1230161222500160BIB080","doi-asserted-by":"crossref","first-page":"1740020","DOI":"10.1142\/S1230161217400200","volume":"24","author":"Diosi L.","year":"2017","journal-title":"Open Syst. Inform. Dyn."},{"key":"S1230161222500160BIB081","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1134\/S1064562410050133","volume":"82","author":"Holevo A. S.","year":"2010","journal-title":"Doklady Math."},{"key":"S1230161222500160BIB082","doi-asserted-by":"crossref","first-page":"32815","DOI":"10.1038\/srep32815","volume":"6","author":"Lesovik G. B.","year":"2016","journal-title":"Sci. Rep."},{"key":"S1230161222500160BIB083","doi-asserted-by":"crossref","first-page":"165329","DOI":"10.1103\/PhysRevB.74.165329","volume":"74","author":"Basieva I. T.","year":"2006","journal-title":"Phys. Rev. B"},{"key":"S1230161222500160BIB084","doi-asserted-by":"publisher","DOI":"10.1080\/09500340.2011.640949"},{"key":"S1230161222500160BIB085","volume-title":"Quantum theory of open systems","author":"Davies E. B.","year":"1976"},{"key":"S1230161222500160BIB086","doi-asserted-by":"publisher","DOI":"10.1063\/1.526000"},{"key":"S1230161222500160BIB087","doi-asserted-by":"crossref","first-page":"16LT01-(6)","DOI":"10.1088\/1751-8121\/aa6263","volume":"50","author":"Diosi L.","year":"2017","journal-title":"J. Phys. A"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161222500160","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T01:43:20Z","timestamp":1701827000000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161222500160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12]]},"references-count":87,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["10.1142\/S1230161222500160"],"URL":"https:\/\/doi.org\/10.1142\/s1230161222500160","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12]]},"article-number":"2250016"}}