The 4D VUH Universal Entropy Law: A Domain-Invariant Coherence–Information Principle Across Physical Systems

Coherent dynamics appear in neural electrophysiology, gravitational-wave post-merger echoes, quantum decoherence curves, condensed-matter phonon spectra, solar acoustic modes, and geomagnetic fluctuations. Despite differences in scale and physical mechanisms, these systems show remarkably similar information–coherence structure.

This work introduces a 4-dimensional coherence–information manifold and demonstrates that when diverse physical time series are projected into this state space and coarse-grained into Markov chains, their entropy rate converges to a universal constant H* ≈ 1.21 nats per step.

We derive this constant from a coherence-based stochastic differential equation that exhibits a stable informational fixed point arising from the balance of drift and diffusion in a unified coherence field.

This paper provides the theoretical foundation for the 4D VUH Universal Entropy Law. Companion studies (EEG and gravitational-wave echoes; materials and phonon spectra) demonstrate empirical convergence.

All derivations, proofs, and algorithmic details are included in the accompanying Supplementary Information.