{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:45:34Z","timestamp":1773798334560,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2014,5,14]],"date-time":"2014-05-14T00:00:00Z","timestamp":1400025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Motivated by the notion of perceptual error, as a core concept of the perceptual control theory, we propose an action-amplitude model for controlled entropic self-organization (CESO). We present several aspects of this development that illustrate its explanatory power: (i) a physical view of partition functions and path integrals, as well as entropy and phase transitions; (ii) a global view of functional compositions and commutative diagrams; (iii) a local geometric view of the K\u00e4hler\u2013Ricci flow and time-evolution of entropic action; and (iv) a computational view using various path-integral approximations.<\/jats:p>","DOI":"10.3390\/e16052699","type":"journal-article","created":{"date-parts":[[2014,5,14]],"date-time":"2014-05-14T11:22:27Z","timestamp":1400066547000},"page":"2699-2712","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Action-Amplitude Approach to Controlled Entropic Self-Organization"],"prefix":"10.3390","volume":"16","author":[{"given":"Vladimir","family":"Ivancevic","sequence":"first","affiliation":[{"name":"Command and Control, Joint & Operations Analysis Division, Defence Science & TechnologyOrganisation, Adelaide SA 5111, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Darryn","family":"Reid","sequence":"additional","affiliation":[{"name":"Command and Control, Joint & Operations Analysis Division, Defence Science & TechnologyOrganisation, Adelaide SA 5111, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jason","family":"Scholz","sequence":"additional","affiliation":[{"name":"Command and Control, Joint & Operations Analysis Division, Defence Science & TechnologyOrganisation, Adelaide SA 5111, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1126\/science.179.4071.351","article-title":"Feedback: Beyond behaviorism","volume":"179","author":"Powers","year":"1973","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1126\/science.181.4105.1116","article-title":"Behaviorism and feedback control","volume":"181","author":"Powers","year":"1973","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s11071-009-9544-6","article-title":"Crowd behavior dynamics: Entropic path-integral model","volume":"59","author":"Ivancevic","year":"2010","journal-title":"Nonlinear Dyn"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01011714","article-title":"Gibbs and Markov random systems with constraints","volume":"10","author":"Moussouris","year":"1974","journal-title":"J. Stat. Phys"},{"key":"ref_5","unstructured":"Landau, L.D., and Lifshitz, E.M. (1996). Statistical Physics, Butterworth\u2013Heinemann. [3rd ed]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","article-title":"Neural networks and physical systems with emergent collective computational abilities","volume":"79","author":"Hopfield","year":"1982","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF02478259","article-title":"A logical calculus of the ideas immanent in nervous activity","volume":"5","author":"McCullough","year":"1943","journal-title":"Bull. Math. Biophys"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ivancevic, V., and Ivancevic, T. (2008). Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals, Springer.","DOI":"10.1007\/978-3-540-79357-1"},{"key":"ref_9","unstructured":"Nicolis, G., and Prigogine, I. (1977). Self\u2013Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations, Wiley."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ivancevic, V., and Ivancevic, T. (2007). Neuro\u2013Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling, Springer.","DOI":"10.1007\/978-3-540-48396-0"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tian, G., and Zhang, Z. (2013). Regularity of K\u00e4hler-Ricci flows on Fano manifolds, arXiv, math.DG\/1310.5897.","DOI":"10.1515\/crelle.2012.021"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/BF01389058","article-title":"Deformation of K\u00e4hler metrics to K\u00e4hler-Einstein metrics on compact K\u00e4hler manifolds","volume":"81","author":"Cao","year":"1985","journal-title":"Invent. Math"},{"key":"ref_13","first-page":"math\/0607607","article-title":"Ricci Flow and the Poincar\u00e9 Conjecture","volume":"arXiv","author":"Morgan","year":"2007","journal-title":"Clay Math. Monogr"},{"key":"ref_14","unstructured":"Perelman, G. (2002). The entropy formula for the Ricci flow and its geometric applications, arXiv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/0022-1236(81)90050-1","article-title":"Logarithmic Sobolev inequality and the spectrum of Schr\u00f6dinger operators","volume":"42","author":"Rothaus","year":"1981","journal-title":"J. Funct. Anal"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ivancevic, V., and Ivancevic, T. (2009). Quantum Neural Computation, Springer.","DOI":"10.1007\/978-90-481-3350-5"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of state calculations by fast computing machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1103\/RevModPhys.20.367","article-title":"Space\u2013time approach to nonrelativistic quantum mechanics","volume":"20","author":"Feynman","year":"1948","journal-title":"Rev. Mod. Phys"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s11071-011-0227-8","article-title":"Turbulence and shock-waves in crowd dynamics","volume":"68","author":"Ivancevic","year":"2012","journal-title":"Nonlinear Dyn"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/5\/2699\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:11:27Z","timestamp":1760217087000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/5\/2699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,14]]},"references-count":19,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2014,5]]}},"alternative-id":["e16052699"],"URL":"https:\/\/doi.org\/10.3390\/e16052699","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,14]]}}}