{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T16:45:55Z","timestamp":1773765955721,"version":"3.50.1"},"reference-count":81,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2007,4,1]],"date-time":"2007-04-01T00:00:00Z","timestamp":1175385600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2007,4]]},"abstract":"<jats:p>This paper presents a sample of the deep and multiple interplay between discrete and continuous behaviours and the corresponding modellings in physics. The aim of this overview is to show that discrete and continuous features coexist in any natural phenomenon, depending on the scales of observation. Accordingly, different models, either discrete or continuous in time, space, phase space or conjugate space can be considered. Some caveats about their limits of validity and their interrelationships (discretisation and continuous limits) are pointed out. Difficulties and gaps arising from the singular nature of continuous limits and from the information loss accompanying discretisation are discussed.<\/jats:p>","DOI":"10.1017\/s0960129507005944","type":"journal-article","created":{"date-parts":[[2007,5,3]],"date-time":"2007-05-03T17:02:05Z","timestamp":1178211725000},"page":"185-223","source":"Crossref","is-referenced-by-count":34,"title":["The discrete versus continuous controversy in physics"],"prefix":"10.1017","volume":"17","author":[{"given":"ANNICK","family":"LESNE","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,4,1]]},"reference":[{"key":"S0960129507005944_N10722","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.50.988"},{"key":"S0960129507005944_N1018B","first-page":"41","volume-title":"Quantum mechanics: Scientific perspectives on Divine Action","author":"Berry","year":"2001"},{"key":"S0960129507005944_N10700","unstructured":"Longo G. (2002) Laplace, Turing and the \u2018imitation game\u2019 impossible geometry: randomness, determinism and program's in Turing's test. In: Conference on cognition, meaning and complexity, Univ. Roma II."},{"key":"S0960129507005944_N1076D","unstructured":"Mielke A. and Zelik S. (2004) Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction-diffusion systems in R n (preprint available at http:\/\/www.iadm.uni-stuttgart.de\/LstAnaMod\/Mielke)."},{"key":"S0960129507005944_N10644","volume-title":"Invariances d'\u00e9chelle","author":"Lagu\u00ebs","year":"2003"},{"key":"S0960129507005944_N107C1","doi-asserted-by":"publisher","DOI":"10.1016\/0960-0779(94)90016-7"},{"key":"S0960129507005944_N106B5","doi-asserted-by":"publisher","DOI":"10.1063\/1.881363"},{"key":"S0960129507005944_N10559","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.62.251"},{"key":"S0960129507005944_N10545","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0983-6"},{"key":"S0960129507005944_N1052B","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"S0960129507005944_N10502","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-004-2271-y"},{"key":"S0960129507005944_N1049C","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/17\/6\/R01"},{"key":"S0960129507005944_N10433","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.52.3525"},{"key":"S0960129507005944_N10336","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.53.643"},{"key":"S0960129507005944_N10313","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2004.01.013"},{"key":"S0960129507005944_N102FF","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511628870"},{"key":"S0960129507005944_N10262","doi-asserted-by":"publisher","DOI":"10.1007\/BF02183610"},{"key":"S0960129507005944_N106D2","volume-title":"Renormalization methods","author":"Lesne","year":"1998"},{"key":"S0960129507005944_N1023E","unstructured":"Castiglione P. , Falcioni M. , Lesne A. and Vulpiani A. (2007) Chaos and coarse-grainings in non equilibrium statistical mechanics, Springer-Verlag (to appear)."},{"key":"S0960129507005944_N1065E","volume-title":"Theory of elasticity","author":"Landau","year":"1984"},{"key":"S0960129507005944_N105D0","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.44.8051"},{"key":"S0960129507005944_N10411","volume-title":"Encyclopedia of Nonlinear Science","author":"Gaspard","year":"2004"},{"key":"S0960129507005944_N1039B","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.044101"},{"key":"S0960129507005944_N10880","doi-asserted-by":"publisher","DOI":"10.1007\/BF01646553"},{"key":"S0960129507005944_N10846","doi-asserted-by":"publisher","DOI":"10.1007\/BF01303805"},{"key":"S0960129507005944_N103EF","volume-title":"Encyclopedia of Nonlinear Science","author":"Gaspard","year":"2004"},{"key":"S0960129507005944_N10376","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-4365-3_14"},{"key":"S0960129507005944_N100B2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-67592-8_9"},{"key":"S0960129507005944_N1082C","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139173049"},{"key":"S0960129507005944_N108EB","doi-asserted-by":"crossref","unstructured":"Shannon C. (1949) Communication in the presence of noise. Proceedings of the IRE 37 10\u201321. (Reprinted in Proceedings of the IEEE 86 447\u2013457 (1998).)","DOI":"10.1109\/JRPROC.1949.232969"},{"key":"S0960129507005944_N10479","doi-asserted-by":"publisher","DOI":"10.1007\/BF01020607"},{"key":"S0960129507005944_N106E6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626302"},{"key":"S0960129507005944_N10456","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(93)90012-3"},{"key":"S0960129507005944_N10863","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.56.405"},{"key":"S0960129507005944_N1096C","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/LIX.236.433"},{"key":"S0960129507005944_N10114","volume-title":"Logique et interaction: pour une g\u00e9om\u00e9trie de la cognition","author":"Bailly","year":"2004"},{"key":"S0960129507005944_N1070E","volume-title":"Modern theory of critical phenomena","author":"Ma","year":"1976"},{"key":"S0960129507005944_N10698","volume-title":"Electromagnetism of continuous media","author":"Landau","year":"1984"},{"key":"S0960129507005944_N104C5","doi-asserted-by":"publisher","DOI":"10.1063\/1.1475765"},{"key":"S0960129507005944_N1078D","doi-asserted-by":"crossref","DOI":"10.1007\/b98868","volume-title":"Mathematical biology","author":"Murray","year":"2002"},{"key":"S0960129507005944_N1059F","doi-asserted-by":"publisher","DOI":"10.1007\/BF01199431"},{"key":"S0960129507005944_N108B1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.48.571"},{"key":"S0960129507005944_N102E5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-57758-1"},{"key":"S0960129507005944_N1022C","unstructured":"Cardy J. (2004) Field theory and nonequilibrium statistical mechanics. Lecture notes available online at http:\/\/www.thphys.physics.ox.ac.uk\/users\/JohnCardy\/home.html."},{"key":"S0960129507005944_N100FA","volume-title":"Complexity. Hierarchical structures and scaling in physics","author":"Badii","year":"1999"},{"key":"S0960129507005944_N109C9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198507895.001.0001","volume-title":"Fluctuations and scaling in biology","author":"Vicsek","year":"2001"},{"key":"S0960129507005944_N10353","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.57.617"},{"key":"#cr-split#-S0960129507005944_N105F3.1","unstructured":"6. Kolmogorov A. N. and Tikhomirov V. M. (1959) \u03b5-entropy and \u03b5-capacity of sets in functional space. Russian Mathematical Surveys 2 277-364. (Translated in Translations Am. Math. Soc. (1961) 17 277-364"},{"key":"#cr-split#-S0960129507005944_N105F3.2","unstructured":"7. also available in Shiryayev, A. N. (ed.) (1993) in Selected works of A. N. Kolmogorov, Vol. III, Kluwer 86-170.)"},{"key":"S0960129507005944_N1016B","volume-title":"Asymptotic analysis for periodic structures","author":"Bensoussan","year":"1978"},{"key":"S0960129507005944_N101C3","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(01)00025-4"},{"key":"S0960129507005944_N10801","volume-title":"Topics in ergodic theory","author":"Parry","year":"1981"},{"key":"S0960129507005944_N10815","volume-title":"Les m\u00e9thodes nouvelles de la m\u00e9canique c\u00e9leste","author":"Poincar\u00e9","year":"1892"},{"key":"S0960129507005944_N108CE","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb00917.x"},{"key":"S0960129507005944_N10745","volume-title":"Fractals: form, chance and dimension","author":"Mandelbrot","year":"1977"},{"key":"S0960129507005944_N1090C","volume-title":"Introduction to percolation theory","author":"Stauffer","year":"1992"},{"key":"S0960129507005944_N10929","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.056202"},{"key":"S0960129507005944_N10949","doi-asserted-by":"publisher","DOI":"10.1063\/1.1350439"},{"key":"S0960129507005944_N109A6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.74.4412"},{"key":"S0960129507005944_N109DD","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1103\/RevModPhys.50.221","article-title":"General properties of entropy","volume":"50","author":"Werhl","year":"1978","journal-title":"Rev. Mod. Phys."},{"key":"S0960129507005944_N1013C","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139170864"},{"key":"S0960129507005944_N109FA","doi-asserted-by":"crossref","unstructured":"Zaks M. and Pikovsky A. (2003) Dynamics at the border of chaos and order. In: Livi, R. and Vulpiani, A. (eds.) The Kolmogorov legacy in physics 61\u201382.","DOI":"10.1007\/978-3-540-39668-0_3"},{"key":"S0960129507005944_N10A12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)00271-Q"},{"key":"S0960129507005944_N1029F","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.65.851"},{"key":"S0960129507005944_N100D7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00709485"},{"key":"S0960129507005944_N103C7","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139170666","volume-title":"Turbulence: The legacy of A. N. Kolmogorov","author":"Frisch","year":"1995"},{"key":"S0960129507005944_N101F2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1986.4767851"},{"key":"S0960129507005944_N10582","first-page":"157","article-title":"Dimension und ausseres Mass","volume":"29","author":"Hausdorff","year":"1919","journal-title":"Math. Ann."},{"key":"S0960129507005944_N1067B","volume-title":"Hydrodynamics","author":"Landau","year":"1984"},{"key":"S0960129507005944_N104EE","volume-title":"Physics and fractal structures","author":"Gouyet","year":"1996"},{"key":"S0960129507005944_N10285","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511549755"},{"key":"S0960129507005944_N10989","doi-asserted-by":"crossref","unstructured":"Turing A. M. (1952) The chemical basis of morphogenesis. Phil. Trans. R. Soc. London B 237 37\u201372. (Reprinted in Saunders, P. T. (ed.) (1992) Collected works of A. M. Turing, vol. 2, North Holland.)","DOI":"10.1098\/rstb.1952.0012"},{"key":"S0960129507005944_N10621","doi-asserted-by":"publisher","DOI":"10.1119\/1.1514233"},{"key":"S0960129507005944_N107A4","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/64\/7\/202"},{"key":"S0960129507005944_N102C2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.53.R5545"},{"key":"S0960129507005944_N107E4","first-page":"617","article-title":"Certain topics in telegraph transmission theory","volume":"47","author":"Nyquist","year":"1928","journal-title":"AIEE Trans."},{"key":"S0960129507005944_N10159","doi-asserted-by":"crossref","unstructured":"Balian R. (2004) Entropy, a protean concept. In: Dalibard, J., Duplantier, B. and Rivasseau, V. (eds.) Poincar\u00e9 Seminar 2003, Birkha\u00fcser.","DOI":"10.1007\/978-3-0348-7932-3_7"},{"key":"S0960129507005944_N105BC","volume-title":"Papers on probability, statistics and statistical physics","author":"Jaynes","year":"1989"},{"key":"S0960129507005944_N1020F","doi-asserted-by":"publisher","DOI":"10.1007\/BF01446819"},{"key":"S0960129507005944_N10759","volume-title":"The fractal geometry of Nature","author":"Mandelbrot","year":"1977"},{"key":"S0960129507005944_N103DB","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02377-8"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129507005944","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T02:22:47Z","timestamp":1707877367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129507005944\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,4]]},"references-count":81,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,4]]}},"alternative-id":["S0960129507005944"],"URL":"https:\/\/doi.org\/10.1017\/s0960129507005944","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,4]]}}}