{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T17:15:08Z","timestamp":1772644508545,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"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>We study a variety of stochastic contact processes\u2014directly related to models of rumor and disease spreading\u2014from the viewpoint of their constants of motion, either exact or approximated. As in deterministic systems, constants of motion in stochastic dynamics make it possible to reduce the number of relevant variables, thereby confining the set of accessible states and facilitating analytical treatment. For processes of rumor propagation based on the Maki\u2013Thompson model, we show how to construct exact constants of motion as linear combinations of conserved quantities in each elementary contact event, and how they relate to the constants of motion of the corresponding mean-field equations, which are obtained as the continuous-time, large-size limit of the stochastic process. For SIR epidemic models, both in homogeneous systems and on heterogeneous networks, we find that a similar procedure produces approximate constants of motion, whose average value is preserved along the evolution. We also give examples of exact and approximate constants of motion built as nonlinear combinations of the relevant variables, whose expressions are suggested by their mean-field counterparts.<\/jats:p>","DOI":"10.3390\/e28030276","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T14:06:56Z","timestamp":1772460416000},"page":"276","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exact and Approximate Constants of Motion in Stochastic Contact Processes"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0681-0592","authenticated-orcid":false,"given":"Dami\u00e1n H.","family":"Zanette","sequence":"first","affiliation":[{"name":"Centro At\u00f3mico Bariloche and Instituto Balseiro, Comisi\u00f3n Nacional de Energ\u00eda At\u00f3mica, Universidad Nacional de Cuyo, Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas, San Carlos de Bariloche 8400, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1787-7082","authenticated-orcid":false,"given":"Eric A.","family":"Roz\u00e1n","sequence":"additional","affiliation":[{"name":"Centro At\u00f3mico Bariloche and Instituto Balseiro, Comisi\u00f3n Nacional de Energ\u00eda At\u00f3mica, Universidad Nacional de Cuyo, Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas, San Carlos de Bariloche 8400, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Arnold, V.I. 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