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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.02329 |
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| _version_ | 1866914237439279104 |
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| author | Caraffa, Laurent |
| author_facet | Caraffa, Laurent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02329 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints Caraffa, Laurent Computer Vision and Pattern Recognition 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. |
| title | BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2601.02329 |