{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:41:32Z","timestamp":1760218892998,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T00:00:00Z","timestamp":1393286400000},"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>We show that a special entropic quantifier, called the statistical complexity, becomes maximal at the transition between super-Poisson and sub-Poisson regimes. This acquires important connotations given the fact that these regimes are usually associated with, respectively, classical and quantum processes.<\/jats:p>","DOI":"10.3390\/e16031178","type":"journal-article","created":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T11:06:23Z","timestamp":1393326383000},"page":"1178-1190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fluctuations, Entropic Quantifiers and Classical-Quantum Transition"],"prefix":"10.3390","volume":"16","author":[{"given":"Flavia","family":"Pennini","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica La Plata\u2013CCT-CONICET, Universidad Nacional de La Plata, C.C. 727, 1900, La Plata, Argentina"},{"name":"Departamento de F\u00edsica, Universidad Cat\u00f3lica del Norte, Av. Angamos 0610, Antofagasta, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelo","family":"Plastino","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica La Plata\u2013CCT-CONICET, Universidad Nacional de La Plata, C.C. 727, 1900, La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0375-9601(95)00867-5","article-title":"A statistical measure of complexity","volume":"209","author":"Mancini","year":"1995","journal-title":"Phys. Lett. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/S0375-9601(97)00855-4","article-title":"Measures of statistical complexity: Why?","volume":"238","author":"Feldman","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.physa.2003.11.005","article-title":"Intensive entropic non-triviality measure","volume":"334","author":"Lamberti","year":"2004","journal-title":"Physica A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.physa.2005.11.053","article-title":"Generalized statistical complexity measures: Geometrical and analytical properties","volume":"369","author":"Plastino","year":"2006","journal-title":"Physica A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0167-2789(94)90273-9","article-title":"The calculi of emergence: Computation, dynamics and induction","volume":"75","author":"Crutchfield","year":"1994","journal-title":"Physica D"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1016\/S0375-9601(96)00756-6","article-title":"Some features of the L\u00f3pez Ruiz-Mancini-Calbet (LMC) statistical measure of complexity","volume":"223","author":"Anteneodo","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"062101","DOI":"10.1103\/PhysRevA.79.062101","article-title":"Arrival times, complex potentials, and decoherent histories","volume":"79","author":"Halliwell","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"032328","DOI":"10.1103\/PhysRevA.79.032328","article-title":"Quantum-classical crossover of a field mode","volume":"79","author":"Everitt","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1142\/S0218127403007977","article-title":"Classical limit and chaotic regime in a semi-quantum Hamiltonian","volume":"13","author":"Kowalski","year":"2003","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/S0375-9601(03)00470-5","article-title":"Wavelet statistical complexity analysis of classical limit","volume":"311","author":"Kowalski","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1103\/PhysRevE.57.1489","article-title":"Chaos in time-dependent variational approximations to quantum dynamics","volume":"57","author":"Cooper","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2596","DOI":"10.1103\/PhysRevA.58.2596","article-title":"Quantitative indicator for semiquantum chaos","volume":"58","author":"Kowalski","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/S0375-9601(02)00034-8","article-title":"Classical limits","volume":"297","author":"Kowalski","year":"2002","journal-title":"Phys. Lett. A"},{"key":"ref_14","first-page":"67","article-title":"Chaos and complexity in the classical-quantum transition","volume":"26","author":"Kowalski","year":"2012","journal-title":"Int. J. Appl. Math. Stat"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5375","DOI":"10.1016\/j.physa.2012.06.012","article-title":"The Tsallis-complexity of a semiclassical time-evolution","volume":"391","author":"Kowalski","year":"2012","journal-title":"Physica A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1126\/science.269.5221.198","article-title":"Observation of Bose-Einstein condensation in a dilute atomic vapor","volume":"269","author":"Anderson","year":"1995","journal-title":"Science"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3969","DOI":"10.1103\/PhysRevLett.75.3969","article-title":"Bose-Einstein condensation in a gas of sodium atoms","volume":"75","author":"Davis","year":"1995","journal-title":"Phys. Rev. Lett"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1103\/PhysRevLett.78.985","article-title":"Bose-Einstein condensation of lithium: Observation of limited condensate number","volume":"78","author":"Bradley","year":"1997","journal-title":"Phys. Rev. Lett"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zachos, C.K., Fairlie, D., and Curtright, T. (2005). Quantum Mechanics in Phase Space, World Scientific.","DOI":"10.1142\/5287"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2766","DOI":"10.1103\/PhysRev.131.2766","article-title":"Coherent and incoherent states of the radiation field","volume":"131","author":"Glauber","year":"1963","journal-title":"Phys. Rev"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1103\/PhysRev.72.26","article-title":"Ionization yield of radiations. II. The fluctuations of the number of ions","volume":"72","author":"Fano","year":"1947","journal-title":"Phys. Rev"},{"key":"ref_22","unstructured":"Frieden, B.R. (2008). Science from Fisher Information, Cambridge University Press. [2nd ed]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1590\/S0103-97332009000400029","article-title":"Note on semiclassical uncertainty relations","volume":"39","author":"Olivares","year":"2009","journal-title":"Braz. J. Phys"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"057101","DOI":"10.1103\/PhysRevE.69.057101","article-title":"Heisenberg-Fisher thermal uncertainty measure","volume":"69","author":"Pennini","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.3390\/e14112081","article-title":"Temperature effects, Frieden-Hawkins\u2019 order-measure, and Wehrl entropy","volume":"14","author":"Pennini","year":"2012","journal-title":"Entropy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4665","DOI":"10.1103\/PhysRevE.62.4665","article-title":"Entropy and Wigner functions","volume":"62","author":"Manfredi","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_27","unstructured":"Tsallis, C. (2008). Introduction to Nonextensive Statistical Mechanics, Springer."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"012119","DOI":"10.1103\/PhysRevA.86.012119","article-title":"Tsallis entropy in phase-space quantum mechanics","volume":"86","author":"Sadeghi","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Scully, M.O., and Zubairy, M.S. (1997). Quantum Optics, Cambridge University Press.","DOI":"10.1017\/CBO9780511813993"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1088\/0954-8998\/6\/5\/001","article-title":"Subcoherent P-representation for non-classical photon states","volume":"6","author":"Brif","year":"1994","journal-title":"Quantum Opt"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Mandel, L., and Wolf, E. (1995). Optical Coherence and Quantum Optics, Cambridge University Press.","DOI":"10.1017\/CBO9781139644105"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gardiner, C.W. (1991). Quantum Noise, Springer.","DOI":"10.1007\/978-3-662-09642-0"},{"key":"ref_33","unstructured":"Carmichael, H.J. (2010). Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations, Springer."},{"key":"ref_34","first-page":"264","article-title":"Some formal properties of the density matrix","volume":"22","author":"Husimi","year":"1940","journal-title":"Proc. Phys. Math. Soc. Jpn"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Agarwal, G.S. (2013). Quantum Optics, Cambirge Universit Press.","DOI":"10.1017\/CBO9781139035170"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1103\/PhysRev.40.749","article-title":"On the quantum correction for thermodynamic equilibrium","volume":"40","author":"Wigner","year":"1932","journal-title":"Phys. Rev"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1140\/epjd\/e2010-00233-2","article-title":"Smoothed Wigner-distributions, decoherence, and the temperature-dependence of the classical-quantum frontier","volume":"61","author":"Pennini","year":"2011","journal-title":"Eur. Phys. J. D"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1051\/epn:2005614","article-title":"Entropy and statistical complexity in brain activity","volume":"36","author":"Plastino","year":"2005","journal-title":"Europhys. News"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Arbona, A., Bona, C., Mi\u00f1ano, B., and Plastino, A. (2013). Statistical complexity measures as telltale of relevant scales in emergent dynamics of spatial systems. arXiv-cond-mat:13111337.","DOI":"10.1016\/j.physa.2014.05.005"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/3\/1178\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:08:37Z","timestamp":1760216917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/3\/1178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,25]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,3]]}},"alternative-id":["e16031178"],"URL":"https:\/\/doi.org\/10.3390\/e16031178","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2014,2,25]]}}}