What question did this study set out to answer?

The aim is to define a foundational law that governs adaptation in various systems based on energy and coherence trade-offs.

February 2, 2026Open Access

The PANMENZ-Law of the Energy Coherence Trade-off

Key Points

The aim is to define a foundational law that governs adaptation in various systems based on energy and coherence trade-offs.
Develop a theoretical framework for the PANMENZ² Law.
Formulate a mathematical inequality describing energy and coherence relationships.
Discuss implications across neural, cognitive, and cultural scales.
Establishes a law stating energy expenditure must be balanced by coherence gains over time.
Provides a unifying perspective on adaptation and stability across multiple domains.

Abstract

This preprint introduces the PANMENZ² Law of the Energy–Coherence Trade‑off, a minimal foundational formulation of a general dynamical constraint governing adaptive systems across neural, cognitive, agentive, social, and cultural scales. The law states that adaptive systems regulate their evolution such that an energy‑dimensioned functional, F(t) = E(t) − λ·C(t), does not increase over time. This inequality formalizes the principle that energy expenditure and structural complexity are permissible only when compensated by coherence gain. The PANMENZ² Law provides a unifying energetic perspective on stability, adaptation, and coherence across multiple domains and establishes the conceptual and mathematical core for future operator‑based and multi‑scale extensions. This work provides a theoretical and mathematical formulation rather than an empirical study.

Read Full Paperexternally

KI fragen

Bookmark

View Full Paper