{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T09:59:04Z","timestamp":1775555944251,"version":"3.50.1"},"reference-count":85,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2013,8,29]],"date-time":"2013-08-29T00:00:00Z","timestamp":1377734400000},"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>What is information? What role does information entropy play in this information exploding age, especially in understanding emergent behaviors of complex systems? To answer these questions, we discuss the origin of information entropy, the difference between information entropy and thermodynamic entropy, the role of information entropy in complexity theories, including chaos theory and fractal theory, and speculate new fields in which information entropy may play important roles.<\/jats:p>","DOI":"10.3390\/e15093396","type":"journal-article","created":{"date-parts":[[2013,8,29]],"date-time":"2013-08-29T12:45:08Z","timestamp":1377780308000},"page":"3396-3418","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":63,"title":["Information Entropy As a Basic Building Block of Complexity Theory"],"prefix":"10.3390","volume":"15","author":[{"given":"Jianbo","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering and China-Asean Research Institute, Guangxi University,100 Daxue Road, Nanning 530005, China"},{"name":"PMB Intelligence LLC, Sunnyvale, CA 94087, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feiyan","family":"Liu","sequence":"additional","affiliation":[{"name":"Management School, University of Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Management School, University of Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and China-Asean Research Institute, Guangxi University,100 Daxue Road, Nanning 530005, China"},{"name":"PMB Intelligence LLC, Sunnyvale, CA 94087, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinhe","family":"Cao","sequence":"additional","affiliation":[{"name":"PMB Intelligence LLC, Sunnyvale, CA 94087, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1029\/2009EO310001","article-title":"How geoscientists think and learn","volume":"90","author":"Kastens","year":"2009","journal-title":"Eos Trans. Am. Geophys. Union"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1086\/147955","article-title":"On the spiral structure of disk galaxies","volume":"140","author":"Lin","year":"1964","journal-title":"Astrophys. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1088\/0034-4885\/68\/8\/R06","article-title":"Jovian atmospheric dynamics: An update after Galileo and Cassini","volume":"68","author":"Vasavada","year":"2005","journal-title":"Rep. Progr. Phys."},{"key":"ref_4","first-page":"543","article-title":"Emergent phenomena in physics (in Chinese)","volume":"39","author":"Zhang","year":"2010","journal-title":"Physics"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hemelrijk, C.K., and Hildenbrandt, H. (2011). Some causes of the variable shape of flocks of birds. PLoS One, 6.","DOI":"10.1371\/journal.pone.0022479"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1093\/beheco\/arq149","article-title":"Self-organized aerial displays of thousands of starlings: A model","volume":"21","author":"Hildenbrandt","year":"2010","journal-title":"Behav. Ecol."},{"key":"ref_7","first-page":"166","article-title":"Schooling fishes","volume":"66","author":"Shaw","year":"1978","journal-title":"Am. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1145\/37402.37406","article-title":"Flocks, herds and schools: A distributed behavioral model","volume":"21","author":"Reynolds","year":"1987","journal-title":"Comput. Graph."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"D\u2019Orsogna, M.R., Chuang, Y.L., Bertozzi, A.L., and Chayes, L.S. (2006). Self-propelled particles with soft-core interactions: Patterns, stability, and collapse. Phys. Rev. Lett., 96.","DOI":"10.1103\/PhysRevLett.96.104302"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1111\/j.1439-0310.2007.01459.x","article-title":"Self-organized shape and frontal density of fish schools","volume":"114","author":"Hemelrijk","year":"2008","journal-title":"Ethology"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"e054301","DOI":"10.1103\/PhysRevLett.88.054301","article-title":"Minimal model for sand dunes","volume":"88","author":"Kroy","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","unstructured":"Shannon, C.E., and Weaver, W. (1949). The Mathematical Theory of Communication, The University of Illinois Press."},{"key":"ref_13","unstructured":"Khinchin, A.I. (1957). Mathematical Foundations of Information Theory, Courier Dover Publications."},{"key":"ref_14","unstructured":"Deloumeayx, P., and Gorzalka, J.D. (2012). Information Theory: New Research, Nova Science Publishers."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/TIT.1976.1055501","article-title":"On the complexity of finite sequences","volume":"22","author":"Lempel","year":"1976","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1109\/TIT.1978.1055934","article-title":"Compression of individual sequences via variable-rate coding","volume":"24","author":"Ziv","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"R2493","DOI":"10.1103\/PhysRevA.52.R2493","article-title":"Scheme for reducing decoherence in quantum computer memory","volume":"52","author":"Shor","year":"1995","journal-title":"Phys. Rev. A"},{"key":"ref_18","unstructured":"Hamming, R. (1991). The Art of Probability for Scientists and Engineers, Addison-Wesley."},{"key":"ref_19","unstructured":"Levine, R.D., and Tribus, M. (1978). The Maximum Entropy Formalism, MIT Press."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gao, J.B., Cao, Y.H., Tung, W.W., and H, J. (2007). Multiscale Analysis of Complex Time Series\u2014Integration of Chaos and Random Fractal Theory, and Beyond, Wiley Interscience.","DOI":"10.1002\/9780470191651"},{"key":"ref_21","unstructured":"Gatlin, L.L. (1972). Information Theory and the Living System, Columbia University Press."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3178","DOI":"10.1103\/PhysRevLett.83.3178","article-title":"Recurrence time statistics for chaotic systems and their applications","volume":"83","author":"Gao","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0375-9601(00)00304-2","article-title":"On the structures and quantification of recurrence plots","volume":"270","author":"Gao","year":"2000","journal-title":"Phys. Lett. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e016117","DOI":"10.1103\/PhysRevE.73.016117","article-title":"Assessment of long range correlation in time series: How to avoid pitfalls","volume":"73","author":"Gao","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gao, J.B., Hu, J., and Tung, W.W. (2011). Facilitating joint chaos and fractal analysis of biosignals through nonlinear i adaptive filtering. PLoS One, 6.","DOI":"10.1371\/journal.pone.0024331"},{"key":"ref_26","unstructured":"Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, W.H. Freeman and Company."},{"key":"ref_27","unstructured":"Gouyet, J.F. (1995). Physics and Fractal Structures, Springer."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Feder, J. (1988). Fractals, Plenum Press.","DOI":"10.1007\/978-1-4899-2124-6"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Falconer, K.J. (1990). Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons.","DOI":"10.2307\/2532125"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3589","DOI":"10.1103\/PhysRevLett.75.3589","article-title":"Statistical-mechanical foundation of the ubiquity of levy distributions in nature","volume":"75","author":"Tsallis","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/LSP.2008.2009844","article-title":"A new way to model non-stationary sea clutter","volume":"16","author":"Hu","year":"2009","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1007\/BF00734321","article-title":"A fundamental link between system theory and statistical mechanics","volume":"17","author":"Atmanspacher","year":"1987","journal-title":"Found. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2591","DOI":"10.1103\/PhysRevA.28.2591","article-title":"Estimation of the Kolmogorov entropy from a chaotic signal","volume":"28","author":"Grassberger","year":"1983","journal-title":"Phys. Rev. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0167-2789(89)90075-4","article-title":"Finite correlation dimension for stochastic-systems with power-law spectra","volume":"35","author":"Osborne","year":"1989","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/0167-2789(91)90036-9","article-title":"Convergence of the K2 entropy for random noises with power law spectra","volume":"47","author":"Provenzale","year":"1991","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"e066204","DOI":"10.1103\/PhysRevE.74.066204","article-title":"Distinguishing chaos from noise by scale-dependent Lyapunov exponent","volume":"74","author":"Gao","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.chaos.2011.12.004","article-title":"Detecting low-dimensional chaos by the \u201cnoise titration\u201d technique: Possible problems and remedies","volume":"45","author":"Gao","year":"2012","journal-title":"Chaos Solitons Fractals"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1103\/PhysRevLett.82.1132","article-title":"When can noise induce chaos?","volume":"82","author":"Gao","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/s11401-009-0108-3","article-title":"Quantifying dynamical predictability: The pseudo-ensemble approach (in honor of Professor Andrew Majda\u2019s 60th birthday)","volume":"30","author":"Gao","year":"2009","journal-title":"Chin. Ann. Math. Ser. B"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1080\/14697688.2011.580774","article-title":"Multiscale analysis of economic time series by scale-dependent Lyapunov exponent","volume":"13","author":"Gao","year":"2011","journal-title":"Quant. Financ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s11071-011-0281-2","article-title":"Entropy measures for biological signal analysis","volume":"68","author":"Gao","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_43","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_44","doi-asserted-by":"crossref","first-page":"e051104","DOI":"10.1103\/PhysRevE.67.051104","article-title":"Structural information in two-dimensional patterns: Entropy convergence and excess entropy","volume":"67","author":"Feldman","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Emmert-Streib, F. (2010). Statistic complexity: Combining Kolmogorov complexity with an ensemble approach. PLoS One, 5.","DOI":"10.1371\/journal.pone.0012256"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"e046210","DOI":"10.1103\/PhysRevE.86.046210","article-title":"Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach","volume":"86","author":"Zunino","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Torcini, A., Grassberger, P., and Politi, A. (1995). Error propagation in extended chaotic systems. J. Phys. A Math. Gen.","DOI":"10.1088\/0305-4470\/28\/16\/011"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Aurell, E., Boffetta, G., Crisanti, A., Paladin, G., and Vulpiani, A. (1996). Growth of non-infinitesimal perturbations in turbulence. Phys. Rev. Lett.","DOI":"10.1103\/PhysRevLett.77.1262"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0305-4470\/30\/1\/003","article-title":"Predictability in the large: An extension of the concept of Lyapunov exponent","volume":"30","author":"Aurell","year":"1997","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0370-1573(93)90012-3","article-title":"Noise, chaos, and (\u03f5, \u03c4)-entropy per unit time","volume":"235","author":"Gaspard","year":"1993","journal-title":"Phys. Rep."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"e021906","DOI":"10.1103\/PhysRevE.71.021906","article-title":"Multiscale entropy analysis of biological signals","volume":"71","author":"Costa","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_52","unstructured":"Prigogine, I. (1980). From Being to Becoming, W.H. Freeman and Company."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/S0378-4371(98)00514-7","article-title":"Microscopic origins of irreversible macroscopic behavior","volume":"263","author":"Lebowitz","year":"1999","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_54","unstructured":"Feynman, R. (1967). The Character of Physical Law, MIT Press."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Arnold, V.I. (1978). Mathematical Methods of Classical Mechanics, Springer-Verlag.","DOI":"10.1007\/978-1-4757-1693-1"},{"key":"ref_56","unstructured":"Kac, M. (1959). Probability and Related Topics in Physical Sciences, Interscience Publishers."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/S1874-5792(02)80004-0","article-title":"A review of mathematical topics in collisional kinetic theory","volume":"1","author":"Villani","year":"2002","journal-title":"Handb. Math. Fluid Dyn."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"e050601","DOI":"10.1103\/PhysRevLett.89.050601","article-title":"Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales","volume":"89","author":"Wang","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_59","unstructured":"Schrodinger, E. (1946). What is Life?, Macmillan Publishers."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Penrose, R. (1989). The Emperor\u2019s New Mind: Concerning Computers, Minds, and The Laws of Physics, Oxford University Press.","DOI":"10.1093\/oso\/9780198519737.001.0001"},{"key":"ref_61","first-page":"1","article-title":"Three approaches to the quantitative definition of \u201cinformation\u201d","volume":"1","author":"Kolmogorov","year":"1965","journal-title":"Probl. Inf. Transm."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/TIT.1968.1054210","article-title":"Logical basis for information theory and probability theory","volume":"IT-14","author":"Kolmogorov","year":"1968","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1109\/10.966601","article-title":"EEG complexity as a measure of depth of anesthesia for patients","volume":"48","author":"Zhang","year":"2001","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1109\/TBME.2002.804582","article-title":"Quantifying physiological data with Lempel-Ziv complexity: Certain issues","volume":"49","author":"Nagarajan","year":"2002","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_65","unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, Wiley."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"e016209","DOI":"10.1103\/PhysRevE.64.016209","article-title":"Effective normalization of complexity measurements for epoch length and sampling frequency","volume":"64","author":"Rapp","year":"2001","journal-title":"Phys. Rev. E"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"2606","DOI":"10.1109\/TBME.2006.883825","article-title":"Analysis of biomedical signals by the Lempel-Ziv complexity: The effect of finite data size","volume":"53","author":"Hu","year":"2006","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s11571-011-9151-3","article-title":"Complexity measures of brain wave dynamics","volume":"5","author":"Gao","year":"2011","journal-title":"Cogn. Neurodyn."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1089\/cmb.1999.6.125","article-title":"Significantly lower entropy estimates for natural DNA sequences","volume":"6","author":"Loewenstern","year":"1999","journal-title":"J. Comput. Biol."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jtbi.2011.10.016","article-title":"New Markov-Shannon entropy models to assess connectivity quality in complex networks: From molecular to cellular pathway, Parasite-Host, Neural, Industry, and Legal-Social networks","volume":"293","author":"Fernandez","year":"2012","journal-title":"J. Theor. Biol."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Cattani, C. (2012). On the existence of wavelet symmetries in Archaea DNA. Comput. Math. Methods Med.","DOI":"10.1155\/2012\/673934"},{"key":"ref_72","first-page":"1","article-title":"On the fractal geometry of DNA by the binary image analysis","volume":"1","author":"Cattani","year":"2013","journal-title":"Bull. Math. Biol."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Ramakrishnan, N., and Bose, R. (2012). Dipole entropy based techniques for segmentation of introns and exons in DNA. Appl. Phys. Lett.","DOI":"10.1063\/1.4747205"},{"key":"ref_74","unstructured":"Cattani, C. (2012, January 10\u201312). Uncertainty and Symmetries in DNA Sequences. Proceedings of the 4th International Conference on Biomedical Engineering in Vietnam, Ho Chi Minh, Vietnam."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Jani, M., and Azad, R.K. (2013). Information entropy based methods for genome comparison. ACM SIG Bioinform.","DOI":"10.1145\/2500124.2500126"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1037\/1089-2680.7.2.183","article-title":"Whatever happened to information theory in psychology?","volume":"7","author":"Luce","year":"2003","journal-title":"Rev. Gen. Psychol."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1037\/a0026767","article-title":"Psychological entropy: A framework for understanding uncertainty-related anxiety","volume":"119","author":"Hirsh","year":"2012","journal-title":"Psychol. Rev."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"6825","DOI":"10.3390\/s120606825","article-title":"Analysis of airborne particulate matter (PM2.5) over Hong Kong using remote sensing and GIS","volume":"12","author":"Shi","year":"2012","journal-title":"Sensors"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Georgescu-Roegen, N. (1971). The Entropy Law and Economic Process, Harvard University Press.","DOI":"10.4159\/harvard.9780674281653"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2307\/1884513","article-title":"A contribution to the theory of economic growth","volume":"70","author":"Solow","year":"1956","journal-title":"Q. J. Econ."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1111\/j.1475-4932.1956.tb00434.x","article-title":"Economic growth and capital accumulation","volume":"32","author":"Swan","year":"1956","journal-title":"Econ. Record"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0378-4371(03)00591-0","article-title":"Thermodynamic analogies in economics and and finance: Instability of markets","volume":"329","author":"McCauley","year":"2003","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Gao, J.B., Hu, J., Mao, X., Zhou, M., Gurbaxani, B., and Lin, J.W.B. (2011). Entropies of negative incomes, Pareto-distributed loss, and financial crises. PLoS One, 6.","DOI":"10.1371\/journal.pone.0025053"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1016\/j.physa.2009.12.008","article-title":"Stokes integral of economic growth: Calculus and Solow model","volume":"389","author":"Mimkes","year":"2010","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_85","unstructured":"Manyika, J., Chui, M., Brown, B., Bughin, J., Dobbs, R., Roxburgh, C., and Byers, A.H. Big data: The next frontier for innovation, competition, and productivity. Available online: http:\/\/www.mckinsey.com\/insights\/business technology\/big data the next frontier for innovation."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/9\/3396\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:56Z","timestamp":1760219336000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/9\/3396"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,29]]},"references-count":85,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2013,9]]}},"alternative-id":["e15093396"],"URL":"https:\/\/doi.org\/10.3390\/e15093396","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8,29]]}}}