The Inaccessible Game

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: $\sum_i h_i = C$. We consider maximum entropy production in the game and show that the dynamics exhibit a GENERIC-like structure combining reversible and irreversible components.