提出连续推理的能耗框架，揭示信息维持的热力学代价。
BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints
- 将信息损耗作为核心约束，建立贝叶斯持续推理的热力学模型
- 证明维持精度τ需功率P ≥ γkBT/2，且P∝γ·τ
- 定义三类新问题类别，关联形式系统与热力学奇异性
我们提出BEDS（贝叶斯涌现耗散结构），一个用于分析在能量约束下需持续维持信念的推理系统的正式框架。不同于经典计算模型假设完美记忆并关注一次性计算，BEDS明确将耗散（随时间的信息损失）作为基本约束。我们证明了一个核心结果：以精度τ对抗耗散率γ，所需功率P ≥ γkBT/2，且功率随γ·τ线性增长。这确立了连续推理的基本热力学成本。我们定义了三类问题——可实现型、可维持型和可结晶型——并表明它们与经典可判定性不同。我们提出戈德尔-兰道尔-普里高津猜想，认为形式系统、计算与热力学中的闭包病态具有共同结构。
原文摘要 · Abstract (English)
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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