Energy Coherence Principle - TOWARDS LIFE-KNOWLEDGE

The evolution of biophysical understanding has passed through three paradigms: the Energy Resistance Principle (ERP), the Energy Coherence Principle (ECP), and now the Hinductive Coherence Principle (HCP). Each marks a deepening realization of how life sustains itself against entropy through self-tuning, memory-bearing geometries of flow.

Building on Picard and Murugan’s ERP, which modeled biological health as energy flow constrained by resistance, and extending through the ECP, which reframed vitality as resonance between structure and flux, the HCP introduces hinductance (H) — the fourth circuit element discovered by Anirban Bandyopadhyay. This element produces magnetic vortex flux proportional to the rate of change of stored charge, embedding geometric memory and adaptive learning into the dynamics of energy transformation.

The inclusion of hinductance completes the universal impedance equation:

Z_eff= R + j(ωL – 1/ωC + ω²H)

Here, resistance (R), inductance (L), capacitance (C), and hinductance (H) co-define a system’s total impedance (Z) and phase relationship (θ), with coherence efficiency (η = cos θ) serving as a unifying measure of health, adaptability, and integrity across scales — from mitochondria to societies.

This paper proposes that the HCP offers a universal framework for understanding how energy becomes information and how information becomes meaning. It bridges physics, biology, psychology, and governance through a shared language of impedance, resonance, and feedback memory. By extending hinductive dynamics into socio-ecological and ethical systems, the model redefines sustainability as phase alignment between metabolism, mind, and morality.

Ultimately, the HCP points to a regenerative science of coherence in which resistance is not merely overcome but remembered and transmuted — revealing life, consciousness, and civilization as nested expressions of one cosmic act of self-resonant learning.

The Energy Resistance Principle (ERP), proposed by Picard and Murugan (2025), formalized biological adaptation as a power-law relation between energetic load and system performance, interpreting health and disease through the lens of resistance. While seminal, this model conflates state and rate variables, omits dynamic feedback processes, and treats living systems as static dissipative structures rather than oscillatory resonators.

We therefore introduce the Energy Coherence Principle (ECP), an upgraded formulation grounded in the physics of impedance, reactance, and phase synchronization. The ECP reframes biological and psychological regulation not as energy loss but as energy-meaning alignment:

where Ψ is potential (state), Φ is flow (rate), Z is complex impedance capturing resistive and reactive components, θ is phase lag, and η is coherence efficiency. Systems maintain vitality by minimizing |Z| and θ — optimizing both structure and timing.

This universal framework unites physics, physiology, and sociology under a single law of regenerative design. By distinguishing resistance from impedance, and by introducing the concepts of storage, resonance, and phase alignment, ECP provides a cross-domain grammar for flow optimization — from mitochondrial OXPHOS and neural synchronization to institutional governance and planetary cycles. Empirical pathways for validation are outlined, integrating biophysical phase-coherence measures (Δψ–NADH coupling), cognitive flow metrics (EEG CFC indices), and societal feedback modeling (policy latency, trust synchrony).

Ultimately, the ECP positions coherence — not resistance — as the foundational invariant of living systems, offering a theoretical and practical bridge from cellular energetics to civilizational renewal.