BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints

• URL: http://arxiv.org/abs/2601.02329v2
• Date: Wed, 07 Jan 2026 08:44:10 GMT
• Title: BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints
• Authors: Laurent Caraffa,
• Abstract summary: We introduce BEDS, a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints.<n>We prove a central result linking energy, precision, and dissipation.<n>We propose the Gdel-Landauer-Prigogine conjecture, suggesting that closure pathologies across formal systems, computation, and thermodynamics share a common structure.
• Score: 0.6345523830122167
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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