{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:33:34Z","timestamp":1760243614427,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T00:00:00Z","timestamp":1380240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>We propose here a formal approach to study collective behaviors intended  as coherent sequences of spatial configurations, adopted by agents through various corresponding structures over time. Multiple, simultaneous structures over time and their sequences are called Meta-Structures and establish sequences of spatial configurations considered as emergent on the basis of coherent criteria chosen and detected by an observer. This coherence is represented by patterns of values of the proper mesoscopic variables adopted, i.e., meta-structural properties. We introduce a formal tool, i.e.,  the family of mesoscopic general vectors, defined by the observer, able to detect coherent behaviors like ergodic or quasi-ergodic ones. Such approach aims to provide a general framework to study intrinsically stochastic processes where the \u201cuniversal evolution laws\u201d fail. However, at the same, the system is structured enough to show significant clusters of collective behaviors \u201cinvisible to\u201d simple statistics.<\/jats:p>","DOI":"10.3390\/systems1040050","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T12:42:41Z","timestamp":1380285761000},"page":"50-65","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Emergence as Mesoscopic Coherence"],"prefix":"10.3390","volume":"1","author":[{"given":"Gianfranco","family":"Minati","sequence":"first","affiliation":[{"name":"Italian Systems Society, Via Pellegrino Rossi 42 Milan, I-20161, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ignazio","family":"Licata","sequence":"additional","affiliation":[{"name":"School of Advanced International Studies on Theoretical and non Linear Methodologies of Physics, Bari I-70124, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,9,27]]},"reference":[{"key":"ref_1","unstructured":"Attanasi, A., Cavagna, A., del Castello, L., Giardina, I., Grigera, T.S., Jeli\u0107, A., Melillo, S., Parisi, L., Pohl, O., and Shen, E. 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