Draft:Persistence Theory and The Persistence Equation

• Comment: Almost entirely WP:OR Sophisticatedevening🍷^(talk) 22:26, 28 March 2025 (UTC)

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Persistence Theory

Persistence Theory is a conceptual and mathematical framework developed by Dr. Bill Giannakopoulos in 2024–2025 to model how complex systems preserve structural coherence and informational integrity under conditions of entropy, noise, and stress. The theory draws from principles in biology, information theory, and systems modeling, and has applications in neuroscience, theoretical physics, and artificial intelligence, particularly in the interpretability and stability of large-scale machine learning models.

Origins

Persistence Theory originated in the context of biomedical research, specifically in the study of redox-reversible cysteine switches in neural tissue. These molecular switches enable reversible changes in protein conformation and function, supporting cellular flexibility and repair. Giannakopoulos extended this biological insight by hypothesizing that reversibility plays a general role in preserving the adaptability and resilience of complex systems.

Inspired by Landauer's principle—which states that erasing information is thermodynamically costly—he explored the idea that irreversible information processing may be structurally damaging, while reversible processes support systemic flexibility. This led to a general hypothesis: systems that maintain high levels of internal mutual information are better able to self-correct, restore lost structure, and resist collapse under perturbation.

The Persistence Equation

The central formulation of the theory is the Persistence Equation, which models the dynamics of information retention and systemic resilience. It incorporates four key variables:

η (eta): Reversibility, approximated via mutual information

Q: Internal entropy (level of disorder or internal noise)

T: External or environmental stress

α (alpha): Structural sensitivity or internal fragility

This equation provides a framework for analyzing how systems degrade, stabilize, or recover over time in response to entropy and external challenges.

Key Concepts

Mutual Information as Reversibility

Mutual information is interpreted as a proxy for a system's ability to preserve memory and coherence. High mutual information suggests reversible processes and the capacity to re-enter prior states.

Swing-Back Dynamics

Systems with sufficient redundancy and structural memory can correct entropy-induced errors through iterative processes, enabling them to "swing back" to a previous coherent configuration.

Memory as Repair

In contrast to the view of memory as passive storage, Persistence Theory frames memory as an active, physically embedded repair mechanism, capable of restoring function and structure after degradation.

Applications

Persistence Theory has been proposed as a conceptual tool for:

Modeling interpretability and epistemic stability in large language models (LLMs)

Diagnosing representational drift and reasoning degradation in AI systems

Understanding neurodegenerative processes as informational collapse

Exploring symmetry and conservation as emergent features of persistent structures

Availability

All related publications and theoretical documents are available in the public OSF repository:https://osf.io/wfh4z/

See Also

Landauer's Principle

Mutual Information

Systems Theory

Neural Reversibility

AI Interpretability

References

Giannakopoulos, B. (2025). From Black Box to Glass Box: Persistence Theory in AI Systems. OSF Preprint. https://osf.io/wfh4z/

Giannakopoulos, B. (2025). Origin of Persistence Theory. OSF Archive. https://osf.io/wfh4z/