Foundations of Local Narrative Physics: Five Fundamental Field Equations with World–Region Dependence

Abstract

This work introduces Local Narrative Physics, a formal mathematical framework for modeling narrative coherence within bounded regions of a story world. The central contribution is the formulation of five field equations—narrative momentum conservation, narrative Gauss law, narrative thermodynamic inequality, affective wave propagation, and a narrative uncertainty principle—each defined on a coherent world branch W and a local region Ω⊂W. These equations capture how information density, causal alignment, affective dynamics, and reader–author uncertainty interact to produce locally coherent narrative segments even when global consistency is absent, as in dreams, multi‑world structures, or meta‑fictional transitions. The framework integrates concepts from information theory, statistical estimation, cognitive psychology, and dynamical systems. It incorporates Fisher information I(θ;Ω,W) and chunk capacity Cchunk(W) to model semantic precision and cognitive load, providing quantitative constraints on narrative entropy and uncertainty. The appendices develop functional models for chunk‑based cognition, operator‑level rigor for narrative phase spaces, boundary conditions for meta‑structural transitions, and algorithms for dynamically estimating Fisher information and chunk capacity within simulation environments. This theoretical structure is intended not only for narrative analysis but also as a consistency‑governing module for future world models, cognitive architectures, and generative systems. As AI systems expand beyond physical world modeling into subjective cognition, imagination, and dream‑like simulation spaces, Local Narrative Physics offers a principled mechanism for maintaining semantic coherence across diverse experiential domains.