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

arXiv: https://arxiv.org/abs/2601.02329 · HTML: https://mlsanity.com/paper/2601.02329/

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- First posted on arXiv 5 Jan 2026.

## Abstract (arXiv)

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 ≥ γ krm B T / 2, with scaling P propto γ · 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 G"odel-Landauer-Prigogine conjecture, suggesting that closure pathologies across formal systems, computation, and thermodynamics share a common structure.