{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T16:14:44Z","timestamp":1772554484456,"version":"3.50.1"},"reference-count":75,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:00:00Z","timestamp":1772150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Dissipative systems that evolve on time-dependent domains occur across systems science whenever redistribution, loss, and global restructuring are coupled with geometric change. This work develops a phenomenological, system-level framework for analyzing such processes and focuses on invariant organizational constraints rather than on microscopic mechanisms or specific physical realizations. Redistribution on an evolving domain is modeled through a diffusion\u2013dissipation equation with curvature- and volume-dependent dissipative loss terms, interpreted as effective drivers of irreversible reorganization. Lie symmetry analysis reveals a non-semisimple structure whose generators act as invariants of admissible system-level reorganizations rather than as sources of conservation laws. By selecting a symmetry-compatible subalgebra, an emergent geometric representation is constructed that compactly encodes global balance constraints without invoking a physical spacetime interpretation. The framework yields time-independent geometric invariants and a system-level balance relation that stabilizes global organization despite ongoing local dissipation. A dimensionless geometric indicator is introduced to quantify intrinsic anisotropy of reorganization and to classify dissipative regimes. Owing to its invariant and phenomenological character, the approach is applicable to a broad class of complex systems with evolving domains and irreversible dynamics, consistent with the scope of systems research.<\/jats:p>","DOI":"10.3390\/systems14030248","type":"journal-article","created":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:52:38Z","timestamp":1772207558000},"page":"248","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["System-Level Invariants and Geometric Balance Relations in Dissipative Dynamics of Merging Domains: A Phenomenological Framework for Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2759-5329","authenticated-orcid":false,"given":"Alin Gilbert","family":"Sumedrea","sequence":"first","affiliation":[{"name":"Department of Psychology, Lucian Blaga University of Sibiu, 550024 Sibiu, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristian Mihai","family":"Sumedrea","sequence":"additional","affiliation":[{"name":"Department of Psychology, Lucian Blaga University of Sibiu, 550024 Sibiu, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"eadt9311","DOI":"10.1126\/sciadv.adt9311","article-title":"Topological classification of driven-dissipative nonlinear systems","volume":"11","author":"Villa","year":"2025","journal-title":"Sci. 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