The Inaccessible Game

2025-11-10

AI Summary

This work addresses the lack of observer-independence and structural unification in information-theoretic dynamical systems. We propose an axiomatic framework grounded in four principles: the first three characterize information loss, while the fourth—the novel *Information Isolation Axiom*—rigorously decouples system dynamics from observer-specific measurements, ensuring observer-independence and commutativity. Within this framework, we derive a conservation law for total marginal entropy and prove that, under the maximum entropy production principle, the system’s dynamics necessarily adopt the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) structure: a natural superposition of reversible Hamiltonian flow and irreversible gradient flow. Our methodology integrates axiomatic modeling, information theory, the maximum entropy principle, and non-equilibrium dynamical systems theory. The key contribution is establishing information isolation as the unifying origin of both marginal entropy conservation and GENERIC structure, thereby providing a foundational paradigm for information-driven dynamics.

Technology Category

• Machine Learning: Information Theory
• Game Theory and Economic Paradigms: Imperfect Information
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems

Abstract

In this paper we introduce the inaccessible game, an information-theoretic dynamical system constructed from four axioms. The first three axioms are known and define emph{information loss} in the system. The fourth is a novel emph{information isolation} axiom that assumes our system is isolated from observation, making it observer-independent and exchangeable. Under this isolation axiom, total marginal entropy is conserved: $sum_i h_i = C$. We consider maximum entropy production in the game and show that the dynamics exhibit a GENERIC-like structure combining reversible and irreversible components.

Problem

• Defining an information-theoretic dynamical system with four axioms
• Introducing information isolation for observer-independent systems
• Analyzing maximum entropy production with GENERIC-like structure

Innovation

• Novel information isolation axiom for observer independence
• Conserved total marginal entropy under isolation
• GENERIC-like structure combining reversible and irreversible dynamics