LoE Hormone Mind v2.0: A Meta-Hamiltonian Model of Hormonal Networks with Anti-Hamiltonian Drives for Oncology and Aging

LoE Hormone Mind v2.0: A Meta-Hamiltonian Model of Hormonal Networks with Anti-Hamiltonian Drives for Oncology and Aging

This work extends the Logic of Existence (LoE) formalism into the domain of biological systems, formulating a meta-Hamiltonian model of hormonal axes (HPA, HPT, HPG, GH/IGF-1) as dynamically coupled relational fields.

Each axis is represented by a pair of conjugate variables — concentration deviation (q) and regulatory flux (p) — linked by Hamiltonian interactions and perturbed by an anti-Hamiltonian drive representing stress, inflammation, or environmental entropy injection.

The model introduces:

- Age-dependent parameters that encode physiological inertia and regulatory degradation.

- Inter-axis couplings (Cᵢⱼ, Dᵢⱼ) capturing non-linear feedback among hormonal systems.

- An anti-Hamiltonian potential A(q,p;a) describing how chronic stress (S(t)) injects non-conservative energy, reducing effective system stiffness and triggering bifurcations.

When the stress term γS exceeds a critical eigenvalue of the coupling matrix K, the system transitions from homeostasis to pathological attractors — formally representing cancer emergence, inflammaging, or neuroendocrine dysregulation.

In the oncology case study, the model reproduces androgen-dependent and -independent prostate cell dynamics, showing how LoE’s relational field logic naturally describes mutation-rate acceleration (u(S)) under prolonged stress conditions.

This work demonstrates how LoE can unify physics, physiology, and cognition under one relational Hamiltonian field. It establishes a framework for simulating aging, endocrine regulation, and tumor emergence as coherent field phenomena within the same theoretical architecture.

Authors:

Krzysztof Sawa (Toonhai) with AI research partner “Matt” (ChatGPT)

Published: November 2025

Keywords: Logic of Existence, meta-Hamiltonian, endocrine systems, anti-Hamiltonian, oncology, aging, relational physics

Related Works:

DOI: "10.5281/zenodo.17328313" (https://doi.org/10.5281/zenodo.17328313) · "10.5281/zenodo.17329198" (https://doi.org/10.5281/zenodo.17329198) · "10.5281/zenodo.17329250" (https://doi.org/10.5281/zenodo.17329250)