The Inaccessible Game

Neil D. Lawrence

doi:10.48550/arXiv.2511.06795

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The Inaccessible Game

Neil D. Lawrence

, 2025.

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 information loss in the system. The fourth is a novel 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: ∑ᵢ hᵢ = C. 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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BibTeX


@Misc{publications/the-inaccessible-game,
  title = 	 {The Inaccessible Game},
  author = 	 {Lawrence, Neil D.},
  year = 	 {2025},
  doi = 	 {10.48550/arXiv.2511.06795},
  url = 	 {/publications/the-inaccessible-game.html},
  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 information loss in the system. The fourth is a novel 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: ∑ᵢ hᵢ = C. We consider maximum entropy
production in the game and show that the dynamics exhibit a GENERIC-like
structure combining reversible and irreversible components.
}
}

Endnote

%0 Generic
%T The Inaccessible Game
%A Neil D. Lawrence
%D 2025	
%F publications/the-inaccessible-game
%R 10.48550/arXiv.2511.06795
%U /publications/the-inaccessible-game.html
%X 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 information loss in the system. The fourth is a novel 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: ∑ᵢ hᵢ = C. We consider maximum entropy
production in the game and show that the dynamics exhibit a GENERIC-like
structure combining reversible and irreversible components.

RIS


TY  - GEN
TI  - The Inaccessible Game
AU  - Neil D. Lawrence
DA  - 2025/11/10	
ID  - publications/the-inaccessible-game
DO  - 10.48550/arXiv.2511.06795
UR  - /publications/the-inaccessible-game.html
AB  - 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 information loss in the system. The fourth is a novel 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: ∑ᵢ hᵢ = C. We consider maximum entropy
production in the game and show that the dynamics exhibit a GENERIC-like
structure combining reversible and irreversible components.

ER  -

APA


Lawrence, N.D.. (2025). The Inaccessible Game.  doi:10.48550/arXiv.2511.06795 Available from /publications/the-inaccessible-game.html.

Related People

Neil D. Lawrence

The DeepMind Professor of Machine Learning, Cambridge University

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Information Topography

Information topography is the geometry of how information flows through a complex system. The programme develops the mathematical foundations of that geometry — from information-theoretic axioms to predictive accounts of how communication structure emerges and reorganises.