Radiation Analytical Derivation of Hysteresis Closure, Evanescent Field Coupling, and Metastable Decay Suppression in Viscoelastic Media

Abstract

This technical report formalizes the analytical and mathematical framework governing the phase transition between an open-hysteresis viscoelastic state (susceptible to delayed Dirac-like impulsive relaxation, stick-slip) and a topologically protected closed-cycle regime mediated by field coupling. By coupling the Maxwell-Minkowski stress tensor with the Kramers-Arrhenius metastable escape formulation, we demonstrate that continuous acoustic beating opens the strain-stress hysteresis loop, accumulating residual plastic/elastic work. We analytically derive how injecting an evanescent electromagnetic mode with pure imaginary normal wavevector (k_z = i*kappa) induces a non-dispersive normal counter-stress at the boundary layer without radiating energy flux. This counter-stress satisfies the exact hysteresis closure condition, driving the escape rate to zero (lambda -> 0, tau_rel -> infinity) and strictly suppressing the discrete impulsive relaxation pulse while preserving the fundamental 13.15 Hz sub-sonic invariant mode.