Gödel-Landauer-Prigogine Conjecture

Establish whether the incompleteness of formal systems, the thermodynamic cost of irreversible computation, and the entropy increase in closed thermodynamic systems are structurally related phenomena by proving or refuting the Gödel-Landauer-Prigogine conjecture, which interprets self-referential constructions as logical entropy, treats Tarski’s hierarchy as an export mechanism, and posits that systems satisfying Openness, Dissipation, and Recursion avoid closure pathologies.

Background

The paper proposes a unifying conjecture connecting foundational limits across logic, computation, and thermodynamics. It suggests that closure pathologies—such as incompleteness in formal systems, energy costs of irreversible computation, and entropy increase in closed thermodynamic systems—share a common structural origin.

Section 6 elaborates the conjecture’s components: logical entropy arising from self-reference, resolution via exporting to meta-levels analogous to entropy export, and the ODR (Openness, Dissipation, Recursion) conditions as a structural framework for avoiding such pathologies.

References

We propose the Gödel-Landauer-Prigogine conjecture, suggesting that closure pathologies across formal systems, computation, and thermodynamics share a common structure.

— BEDS : Bayesian Emergent Dissipative Structures : A Formal Framework for Continuous Inference Under Energy Constraints  (2601.02329 - Caraffa, 5 Jan 2026) in Abstract; Section 6 (The Gödel-Landauer-Prigogine Conjecture)