
TL;DR
This paper introduces the inaccessible game, a novel information-theoretic dynamical system with an isolation axiom, demonstrating a GENERIC-like structure that combines reversible and irreversible dynamics under conservation of total entropy.
Contribution
It proposes a new information isolation axiom and analyzes its implications, revealing a GENERIC-like structure in the dynamics of the system.
Findings
Total marginal entropy is conserved under the isolation axiom
The system exhibits a GENERIC-like structure with reversible and irreversible parts
Maximum entropy production dynamics are characterized in the model
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: . We consider maximum entropy production in the game and show that the dynamics exhibit a GENERIC-like structure combining reversible and irreversible components.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Computability, Logic, AI Algorithms · Mathematical Dynamics and Fractals
