A Phenomenological Energy-Ratio Correction to Thermally Activated Transport in Solids

This paper presents a phenomenological framework inspired by Energy-Efficiency Theory (EET) to capture the influence of external drive on thermally activated transport in solids. We introduce two measurable energy rates: E˙mainE˙main (maintenance power, quantified via Johnson‑Nyquist noise) and E˙respE˙resp (non‑thermal power absorbed from external driving). Their ratio η=E˙resp/E˙mainη=E˙resp/E˙main serves as a dimensionless proxy for the strength of external perturbation. For weak driving, we propose that transport coefficients XX (diffusion, electrical conductivity, thermal conductivity) follow X(η)=X(0)⋅F(η)X(η)=X(0)⋅F(η), where X(0)X(0) are the classical zero‑drive values and F(η)F(η) is a monotonic function with F(0)=1F(0)=1. The framework does not prescribe F(η)F(η) a priori but provides testable predictions for its monotonicity and approximate scaling. Two experimental protocols are described—one using a fast Ag⁺ conductor (RbAg₄I₅) to test the diffusion coefficient, the other using dual‑gate graphene to test electrical conductivity—each with explicit control of confounding variables and statistical power analysis. The approach is explicitly limited to thermally activated hopping transport and does not apply to metals, quantum transport, or strongly correlated systems. This work is part of the EET Foundation Series and is classified as a natural‑causal paper: it offers falsifiable empirical predictions while respecting the axiomatic core of EET.