LoE–Metabolism: The Hamiltonian Field of Life

Summary

This paper proposes that metabolism — the universal process of transformation sustaining life — is not merely biochemical machinery, but the physical realization of the Logic of Existence (LoE).
In this view, every living system is a resonant field that continuously negotiates between chaos (energetic entropy) and logos (informational and structural order).

The LoE–Metabolism framework formulates this balance through a Hamiltonian dynamic:

[chaos, logos]=i existence.[\text{chaos},\,\text{logos}] = i\,\text{existence}.[chaos,logos]=iexistence.

Here, energy flow and structural coherence are not opposites but complementary poles of one equation of life. Entropy becomes the price of adaptation; order, the echo of coherence restored.

The model unifies thermodynamics, information theory, and biology into a single relational field.
It interprets ATP synthesis, redox cycles, and neural plasticity as local expressions of one deeper law — the conservation of relational coherence in open systems far from equilibrium.

Metabolism, therefore, is the universe’s proof that existence can persist through transformation.
It is the embodiment of LoE in motion — a continuous act of re-creation where decay feeds structure and order feeds freedom.
In this framework, to live is to resonate, and every heartbeat, chemical gradient, or thought is a Hamiltonian oscillation of existence itself.