[Paper] BEDS: Bayesian Emergent Dissipative Structures

Source: arXiv - 2601.02329v1

Overview

Laurent Caraffa’s paper introduces BEDS (Bayesian Emergent Dissipative Structures), a unifying theory that treats learning—whether in physics, biology, or software—as a thermodynamic process that turns “flux” (raw data, energy, or uncertainty) into stable “structure” (knowledge, models, or priors). By linking Prigogine’s dissipative‑structure theory with Bayesian updating, the work claims to explain why learning systems must constantly export entropy and offers a concrete, ultra‑energy‑efficient peer‑to‑peer (P2P) architecture as proof‑of‑concept.

Key Contributions

• Theoretical bridge between non‑equilibrium thermodynamics, Bayesian inference, and information geometry.
• Isomorphism proof: Bayesian updating ↔ thermodynamic dissipation, showing that each posterior becomes the next level’s prior in a dissipative cycle.
• Derivation of universal constants (e, π, φ) as fixed points of minimal‑axiom Bayesian inference, suggesting they are inevitable in any uncertainty‑handling system.
• Gödel‑Thermodynamics conjecture: incompleteness/undecidability in formal systems are analogues of entropy‑dissipation deficits in physical processes.
• Practical prototype: a P2P network that embeds BEDS principles, delivering ~10⁶× better energy efficiency than conventional distributed consensus (e.g., proof‑of‑work blockchains) while supporting continuous on‑line learning.
• Roadmap for sustainable AI: outlines how dissipative learning can keep computational growth in check by design.

Methodology

1. Formal Mapping – The author starts from Prigogine’s equations for dissipative structures and rewrites them in the language of Bayesian probability updates.
2. Information‑Geometric Lens – Using the Fisher‑Rao metric, the paper treats posterior distributions as points on a statistical manifold; the “geodesic flow” of learning corresponds to entropy export.
3. Axiomatic Derivation – By imposing only three natural axioms (non‑negativity, normalization, and invariance under re‑parameterization), the author solves the fixed‑point equations of the Bayesian update and shows that e, π, φ naturally arise.
4. Simulation & Prototype – A lightweight P2P overlay is built where each node maintains a local Bayesian model. Nodes exchange sufficient statistics rather than raw data, allowing the network to collectively update a global posterior while each node dissipates entropy through communication cost. Energy consumption is measured against a baseline PoW blockchain and a standard federated‑learning server‑client setup.

The approach stays high‑level enough for developers: think of each node as a micro‑service that continuously refines a probability model and “throws away” uncertainty via cheap message passing instead of heavy mining.

Results & Findings

Key takeaways

• Six orders of magnitude energy savings stem from replacing proof‑of‑work’s irreversible computation with reversible Bayesian updates that naturally export entropy.
• The system maintains convergence even as nodes join/leave, illustrating the robustness of dissipative cycles.
• The emergence of mathematical constants as fixed points validates the theoretical claim that any self‑updating uncertainty system will gravitate toward these values.

Practical Implications

• Green AI: Developers building large‑scale ML pipelines can adopt BEDS‑style message‑passing updates to slash data‑center power draw, especially for edge‑oriented federated learning.
• Decentralized Consensus: Blockchain designers can replace PoW/PoS with Bayesian‑driven consensus, achieving secure agreement with negligible energy cost.
• Adaptive Systems: Robotics, IoT, and autonomous agents can embed BEDS loops to continuously refine models while guaranteeing that each learning step “dissipates” uncertainty, preventing runaway computational growth.
• Explainability: The thermodynamic framing offers a new lens for interpreting model drift—if entropy isn’t being exported (e.g., due to stale priors), the system may become unstable, prompting proactive maintenance.

Limitations & Future Work

• Assumption of idealized communication: The prototype assumes lossless, low‑latency exchanges; real‑world networks may introduce noise that affects entropy accounting.
• Scalability beyond 10⁴ nodes: While linear scaling is shown up to ten thousand nodes, the paper does not explore massive public‑internet deployments.
• Gödel‑Thermodynamics conjecture remains speculative; formal proof or empirical validation is left for later studies.
• Hardware support: Current CPUs/GPUs lack native primitives for reversible Bayesian updates; future work could explore ASICs or neuromorphic chips optimized for BEDS operations.

Overall, BEDS opens a promising interdisciplinary pathway: by treating learning as a dissipative thermodynamic process, developers can design AI systems that are both more sustainable and theoretically grounded. The next steps will be to harden the networking layer, test at internet scale, and integrate BEDS primitives into mainstream ML frameworks.

Authors

• Laurent Caraffa

Paper Information

• arXiv ID: 2601.02329v1
• Categories: cs.CV
• Published: January 5, 2026
• PDF: Download PDF