{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:11:01Z","timestamp":1760148661738,"version":"build-2065373602"},"reference-count":76,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T00:00:00Z","timestamp":1685145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity\u2019s strength (\u03b6). This observation helped us to uncover a hidden connection between active SOC systems and \u03b1-stable Levy systems. We demonstrate that one can partially sweep \u03b1-stable Levy distributions by changing \u03b6. The system undergoes a crossover towards Bak\u2013Tang\u2013Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point \u03b6&lt;\u03b6*\u22480.1.<\/jats:p>","DOI":"10.3390\/e25060861","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:18:43Z","timestamp":1685204323000},"page":"861","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Anomalous Self-Organization in Active Piles"],"prefix":"10.3390","volume":"25","author":[{"given":"Morteza","family":"Nattagh-Najafi","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA"}]},{"given":"Mohammad","family":"Nabil","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA"}]},{"given":"Rafsun Hossain","family":"Mridha","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1059-8806","authenticated-orcid":false,"given":"Seyed Amin","family":"Nabavizadeh","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11167","DOI":"10.1523\/JNEUROSCI.23-35-11167.2003","article-title":"Neuronal avalanches in neocortical circuits","volume":"23","author":"Beggs","year":"2003","journal-title":"J. Neurosci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"028107","DOI":"10.1103\/PhysRevLett.96.028107","article-title":"Self-organized criticality model for brain plasticity","volume":"96","author":"Herrmann","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ribeiro, T.L., Copelli, M., Caixeta, F., Belchior, H., Chialvo, D.R., Nicolelis, M.A., and Ribeiro, S. (2010). Spike avalanches exhibit universal dynamics across the sleep-wake cycle. PLoS ONE, 5.","DOI":"10.1371\/journal.pone.0014129"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"166","DOI":"10.3389\/fnsys.2014.00166","article-title":"Self-organized criticality as a fundamental property of neural systems","volume":"8","author":"Hesse","year":"2014","journal-title":"Front. Syst. Neurosci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108","DOI":"10.3389\/fnsys.2014.00108","article-title":"Spike avalanches in vivo suggest a driven, slightly subcritical brain state","volume":"8","author":"Priesemann","year":"2014","journal-title":"Front. Syst. Neurosci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"639389","DOI":"10.3389\/fphy.2021.639389","article-title":"Self-organized criticality in the brain","volume":"9","author":"Plenz","year":"2021","journal-title":"Front. Phys."},{"key":"ref_7","first-page":"104","article-title":"Nonlinear measures for characterizing rough surface morphologies","volume":"61","author":"Kondev","year":"2000","journal-title":"Phys. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102282","DOI":"10.1016\/j.cis.2020.102282","article-title":"Complexity and self-organized criticality in liquid foams. A short review","volume":"285","author":"Ritacco","year":"2020","journal-title":"Adv. Colloid Interface Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"248301","DOI":"10.1103\/PhysRevLett.103.248301","article-title":"Self-organized criticality in sheared suspensions","volume":"103","author":"Gerbode","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0920-5632(01)01185-9","article-title":"Self-organized criticality in atmospheric cascades","volume":"97","author":"Wodarczyk","year":"2001","journal-title":"Nucl. Phys.-Proc. Suppl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3449","DOI":"10.1175\/JAS-D-12-069.1","article-title":"Self-organized criticality and homeostasis in atmospheric convective organization","volume":"69","author":"Yano","year":"2012","journal-title":"J. Atmos. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"15635","DOI":"10.1029\/JB094iB11p15635","article-title":"Earthquakes as a self-organized critical phenomenon","volume":"94","author":"Bak","year":"1989","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1209\/0295-5075\/9\/3\/002","article-title":"Self-organized criticality and earthquakes","volume":"9","author":"Sornette","year":"1989","journal-title":"EPL Europhys. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6853","DOI":"10.1029\/JB095iB05p06853","article-title":"Earthquakes as self-organized critical phenomena","volume":"95","author":"Ito","year":"1990","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1103\/PhysRevA.43.625","article-title":"Self-organized criticality in a crack-propagation model of earthquakes","volume":"43","author":"Chen","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/S0378-4371(99)00290-3","article-title":"Self-organized percolation model for stock market fluctuations","volume":"271","author":"Stauffer","year":"1999","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"042814","DOI":"10.1103\/PhysRevE.92.042814","article-title":"Modeling financial markets by self-organized criticality","volume":"92","author":"Biondo","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.physa.2004.11.061","article-title":"Self-organized criticality and stock market dynamics: An empirical study","volume":"350","author":"Bartolozzi","year":"2005","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1142\/S0129183102003164","article-title":"Self-organized criticality in a model of collective bank bankruptcies","volume":"13","author":"Aleksiejuk","year":"2002","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3120","DOI":"10.1016\/j.physa.2011.04.017","article-title":"Replicating financial market dynamics with a simple self-organized critical lattice model","volume":"390","author":"Dupoyet","year":"2011","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1155\/S1026022699000151","article-title":"Self-organized criticality and urban development","volume":"3","author":"Batty","year":"1999","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_22","unstructured":"Weisbuch, G., Solomon, S., and Stauffer, D. (2001). Economics with Heterogeneous Interacting Agents, Springer."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1177\/095169280201400203","article-title":"Why do societies collapse? A theory based on self-organized criticality","volume":"14","author":"Brunk","year":"2002","journal-title":"J. Theor. Politics"},{"key":"ref_24","first-page":"65","article-title":"Society as a self-organized critical system","volume":"16","author":"Kron","year":"2009","journal-title":"Cybern. Hum. Knowing"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Aschwanden, M.J. (2012). Self-Organized Criticality Systems in Astrophysics (Chapter 13). arXiv.","DOI":"10.1007\/978-3-642-15001-2"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"032307","DOI":"10.1103\/PhysRevE.96.032307","article-title":"Mechanisms of self-organized criticality in social processes of knowledge creation","volume":"96","author":"Dankulov","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/S0378-4371(98)00057-0","article-title":"Analysis of rainfall records: Possible relation to self-organized criticality","volume":"254","author":"Andrade","year":"1998","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjb\/e2019-100209-8","article-title":"An electronic avalanche model for metal\u2013insulator transition in two dimensional electron gas","volume":"92","author":"Najafi","year":"2019","journal-title":"Eur. Phys. J. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"140504","DOI":"10.1103\/PhysRevB.69.140504","article-title":"Experimental test of the self-organized criticality of vortices in superconductors","volume":"69","author":"Welp","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1140\/epjb\/e2006-00063-7","article-title":"Avalanches and self-organized criticality in superconductors","volume":"50","author":"Wijngaarden","year":"2006","journal-title":"Eur. Phys. J. B-Condens. Matter Complex Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"051306","DOI":"10.1103\/PhysRevE.67.051306","article-title":"Avalanche dynamics, surface roughening, and self-organized criticality: Experiments on a three-dimensional pile of rice","volume":"67","author":"Aegerter","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4950","DOI":"10.1103\/PhysRevLett.78.4950","article-title":"Long-Tailed trapping times and l\u00e9vy flights in a Self-Organized critical granular system","volume":"78","author":"Corral","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","unstructured":"Kinouchi, O. (1998). Self-organized (quasi-) criticality: The extremal Feder and Feder model. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"20002","DOI":"10.1209\/0295-5075\/123\/20002","article-title":"The emergence of weak criticality in SOC systems","volume":"123","author":"Palmieri","year":"2018","journal-title":"Europhys. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"111877","DOI":"10.1016\/j.chaos.2022.111877","article-title":"Homeostatic criticality in neuronal networks","volume":"156","author":"Menesse","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"15682","DOI":"10.1038\/s41598-018-33923-9","article-title":"Homeostatic plasticity and emergence of functional networks in a whole-brain model at criticality","volume":"8","author":"Rocha","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"P06004","DOI":"10.1088\/1742-5468\/2015\/06\/P06004","article-title":"Can dynamical synapses produce true self-organized criticality?","volume":"2015","author":"Copelli","year":"2015","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"P09009","DOI":"10.1088\/1742-5468\/2009\/09\/P09009","article-title":"Self-organization without conservation: True or just apparent scale-invariance?","volume":"2009","author":"Bonachela","year":"2009","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3874","DOI":"10.1038\/s41598-019-40473-1","article-title":"Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems","volume":"9","author":"Kinouchi","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1146\/annurev-conmatphys-070909-104101","article-title":"The mechanics and statistics of active matter","volume":"1","author":"Ramaswamy","year":"2010","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"045006","DOI":"10.1103\/RevModPhys.88.045006","article-title":"Active particles in complex and crowded environments","volume":"88","author":"Bechinger","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"P02029","DOI":"10.1088\/1742-5468\/2011\/02\/P02029","article-title":"Lattice models of nonequilibrium bacterial dynamics","volume":"2011","author":"Thompson","year":"2011","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"168001","DOI":"10.1103\/PhysRevLett.125.168001","article-title":"Self-organized critical coexistence phase in repulsive active particles","volume":"125","author":"Shi","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"11408","DOI":"10.1073\/pnas.1600503113","article-title":"Bursts of activity in collective cell migration","volume":"113","author":"Chepizhko","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"025002","DOI":"10.1088\/1367-2630\/aaa392","article-title":"Avalanche dynamics for active matter in heterogeneous media","volume":"20","author":"Reichhardt","year":"2018","journal-title":"New J. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"235702","DOI":"10.1103\/PhysRevLett.108.235702","article-title":"Athermal phase separation of self-propelled particles with no alignment","volume":"108","author":"Fily","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"030601","DOI":"10.1103\/PhysRevE.98.030601","article-title":"Critical behavior of active Brownian particles","volume":"98","author":"Siebert","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"042119","DOI":"10.1103\/PhysRevE.92.042119","article-title":"Flocking with discrete symmetry: The two-dimensional active Ising model","volume":"92","author":"Solon","year":"2015","journal-title":"Phys. Rev. E"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1038\/nphys3035","article-title":"Information transfer and behavioural inertia in starling flocks","volume":"10","author":"Attanasi","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"050103","DOI":"10.1103\/PhysRevE.80.050103","article-title":"Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles","volume":"80","author":"Baglietto","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"074901","DOI":"10.1063\/1.4975812","article-title":"Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions","volume":"146","author":"Trefz","year":"2017","journal-title":"J. Chem. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"124904","DOI":"10.1063\/1.4963191","article-title":"Vapour-liquid coexistence of an active Lennard-Jones fluid","volume":"145","author":"Prymidis","year":"2016","journal-title":"J. Chem. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/S0378-4371(98)00493-2","article-title":"The abelian sandpile and related models","volume":"263","author":"Dhar","year":"1999","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1103\/PhysRevLett.59.381","article-title":"Self-organized criticality: An explanation of the 1\/f noise","volume":"59","author":"Bak","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"023211","DOI":"10.1088\/1742-5468\/aaa8f0","article-title":"Sandpile on uncorrelated site-diluted percolation lattice; from three to two dimensions","volume":"2018","author":"Najafi","year":"2018","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"051104","DOI":"10.1103\/PhysRevE.85.051104","article-title":"Avalanche frontiers in the dissipative Abelian sandpile model and off-critical Schramm-Loewner evolution","volume":"85","author":"Najafi","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"042402","DOI":"10.1103\/PhysRevE.103.042402","article-title":"Role of anaxonic local neurons in the crossover to continuously varying exponents for avalanche activity","volume":"103","author":"Seifi","year":"2021","journal-title":"Phys. Rev. E"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"184430","DOI":"10.1103\/PhysRevB.74.184430","article-title":"Stretched exponential relaxation arising from a continuous sum of exponential decays","volume":"74","author":"Johnston","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1039\/tf9706600080","article-title":"Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function","volume":"66","author":"Williams","year":"1970","journal-title":"Trans. Faraday Soc."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1063\/1.321639","article-title":"Strain relaxation in glass by optical correlation and pressure jump relaxation","volume":"46","author":"Bucaro","year":"1975","journal-title":"J. Appl. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/0032-3861(75)90188-3","article-title":"Molecular motion in polystyrene-plasticizer systems as studied by dielectric relaxation","volume":"16","author":"Hains","year":"1975","journal-title":"Polymer"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Struik, L.C.E. (1977). Physical Aging in Amorphous Polymers and Other Materials, Citeseer.","DOI":"10.1002\/pen.760170305"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1039\/pr9777400077","article-title":"Studies of molecular motion in liquids and solids using low frequency dielectric relaxation and related techniques","volume":"74","author":"Williams","year":"1977","journal-title":"Annu. Rep. Prog. Chem. Sect. Phys. Inorg. Chem."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.jtbi.2004.10.028","article-title":"Scale-free neurodegeneration: Cellular heterogeneity and the stretched exponential kinetics of cell death","volume":"233","author":"Clarke","year":"2005","journal-title":"J. Theor. Biol."},{"key":"ref_65","unstructured":"Stanley, H.E., and Mantegna, R.N. (2000). An Introduction to Econophysics, Cambridge University Press."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"2766","DOI":"10.1103\/PhysRevLett.68.2766","article-title":"Probability density of velocity increments in turbulent flows","volume":"68","author":"Kailasnath","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"9726","DOI":"10.1002\/2015GL066232","article-title":"Modeling aftershocks as a stretched exponential relaxation","volume":"42","author":"Mignan","year":"2015","journal-title":"Geophys. Res. Lett."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s100510050276","article-title":"Stretched exponential distributions in nature and economy: \u201cFat tails\u201d with characteristic scales","volume":"2","author":"Laherrere","year":"1998","journal-title":"Eur. Phys. J.-Condens. Matter Complex Syst."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1103\/PhysRevE.58.779","article-title":"Dynamic heterogeneity, spatially distributed stretched-exponential patterns, and transient dispersions in solvation dynamics","volume":"58","author":"Richert","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.cam.2006.10.014","article-title":"The role of the Fox\u2013Wright functions in fractional sub-diffusion of distributed order","volume":"207","author":"Mainardi","year":"2007","journal-title":"J. Comput. Appl. Math."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"104201","DOI":"10.1103\/PhysRevB.76.104201","article-title":"Stretched exponential relaxation and ac universality in disordered dielectrics","volume":"76","author":"Milovanov","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1090\/S0002-9904-1946-08672-3","article-title":"The Representation of e\u2212x\u03bb as a Laplace Integral","volume":"52","author":"Pollard","year":"1946","journal-title":"Bull. Am. Math. Soc."},{"key":"ref_73","unstructured":"Artin, E. (2015). The Gamma Function, Courier Dover Publications."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF01770352","article-title":"On L\u00e9vy (or stable) distributions and the Williams-Watts model of dielectric relaxation","volume":"34","author":"Montroll","year":"1984","journal-title":"J. Stat. Phys."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1515\/fca-2017-0014","article-title":"The stretched exponential behavior and its underlying dynamics. The phenomenological approach","volume":"20","author":"Horzela","year":"2017","journal-title":"Fract. Calc. Appl. Anal."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"210604","DOI":"10.1103\/PhysRevLett.105.210604","article-title":"Exact and explicit probability densities for one-sided L\u00e9vy stable distributions","volume":"105","author":"Penson","year":"2010","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/6\/861\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:43:40Z","timestamp":1760125420000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/6\/861"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,27]]},"references-count":76,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["e25060861"],"URL":"https:\/\/doi.org\/10.3390\/e25060861","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,5,27]]}}}