{"ID":2822688,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.02329","arxiv_id":"2601.02329","title":"BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints","abstract":"We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect memory and focus on one-shot computation, BEDS explicitly incorporates dissipation (information loss over time) as a fundamental constraint. We prove a central result linking energy, precision, and dissipation: maintaining a belief with precision $τ$ against dissipation rate $γ$ requires power $P \\geq γk_{\\rm B} T / 2$, with scaling $P \\propto γ\\cdot τ$. This establishes a fundamental thermodynamic cost for continuous inference. We define three classes of problems -- BEDS-attainable, BEDS-maintainable, and BEDS-crystallizable -- and show these are distinct from classical decidability. We propose the Gödel-Landauer-Prigogine conjecture, suggesting that closure pathologies across formal systems, computation, and thermodynamics share a common structure.","short_abstract":"We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect memory and focus on one-shot computation, BEDS explicitly incorporates dissipation...","url_abs":"https://arxiv.org/abs/2601.02329","url_pdf":"https://arxiv.org/pdf/2601.02329v2","authors":"[\"Laurent Caraffa\"]","published":"2026-01-05T18:21:02Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[]","has_code":false}