{
  "abstract": "We develop a whole-trajectory relaxation framework for dissipative evolutions with non-convex, state- and history-dependent kinetics. The framework arises naturally from a game-theoretical formulation of energy--dissipation evolution. State--rate consistency is eliminated by causal Volterra reconstruction, reducing the problem to a diagonal equilibrium condition on complete rate trajectories. We establish a direct method based on vanishing-defect approximability, compactness, and complementary semicontinuity. The relaxation mechanism is computed exactly for a reduced simple-shear model with a non-convex kinetic potential and a local memory variable. The enriched state is a Young measure on complete local histories. We identify explicitly the sequential lower-semicontinuous envelope of the pure diagonal defect, characterize its zero set, construct pure recovery sequences for every relaxed zero, and prove existence through a frozen-best-response time discretization. The resulting coexistence of distinct rate populations with distinct memories provides a reduced mechanism for kinetic shear banding and connects naturally with negative strain-rate sensitivity and dynamic strain aging such as underlie the Portevin--Le Chatelier effect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26484",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Ortiz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aenn1wv7wg7ec.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26484",
  "fulltext_url": null,
  "id": "aenn1wv7wg7ec",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26484",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2505|Microstructure and mechanical properties"
    ]
  ],
  "openalex": "W7204596892",
  "pdf_url": "https://arxiv.org/pdf/2608.26484",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aenn1wv7wg7ec.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.26484",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26484"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Microstructure evolution as a game",
  "title_text": "Microstructure evolution as a game",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/aenn1wv7wg7ec",
  "venue": "arXiv",
  "versions": []
}