Overview
The inaccessible game is deliberately closed and agent-free: marginal entropy conservation $\sum_i h_i = C$ and maximum-entropy production generate an information topography without pre-specified channels. Real organisations and agentic systems are open — they exchange information with an environment. Recent work on steepest entropy ascent in composite systems (Ray and Beretta, 2025) shows how hard it is to open a thermodynamically consistent dynamics without violating no-signaling or smuggling in an external referee. This project asks whether the inaccessible game can be opened in a way that remains internally adjudicable, preserves (a suitable generalisation of) conservation structure, and still produces a reorganising topography under changing external information demand. A rigorous negative result — characterising an obstruction — is an acceptable and publishable outcome.
Prerequisite
L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
FAQs
- What are the prerequisites?
L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
- What will I learn in this Project?
You will learn axiomatic information dynamics, open-system thermodynamics (Lindblad versus top-down steepest-entropy-ascent approaches), and how to test conservation and no-signaling properties numerically. You will practise translating informal modelling choices into precise mathematical rules and identifying when a framework fails cleanly.
- What is the objective of the project?
(1) Formalise at least two candidate openings: controlled marginal-entropy flux to an environment, and a composite-system construction using local perception operators in the spirit of Ray–Beretta SEA. (2) Prove or numerically certify which properties survive (conservation, no-signaling, internal adjudicability, GENERIC structure). (3) Exhibit — or rule out — an open-system topography that reorganises under changing external information demand, with a falsifiable prediction about junction saturation. (4) Document failure modes carefully: if the game collapses when opened, state the obstruction as a theorem-level claim with computational evidence. Deliverables: mathematical note, numerical test suite, and thesis chapter.
- How does this fit into the bigger picture?
The inaccessible game would require an open-system extension before organisational and multi-agent applications can inherit the formal framework. This project attacks that gap directly. It is the most mathematical of the available projects and suits a student comfortable with proofs, differential geometry of statistical manifolds, and careful numerical verification.
