Entropy deformation reveals monotonic tail amplification and instability signatures in gold market dynamics

Extreme fluctuations in complex systems often emerge despite finite variance constraints, challenging conventional stability assumptions. Here, we investigate how entropy-driven deformation alters distributional structure and amplifies tail behavior in finite-variance systems. We demonstrate analytically that entropy perturbations induce a monotonic amplification of effective tail weight while preserving finite second moments, establishing a structural mechanism for instability without divergence. Using gold market dynamics as an empirical testbed, we show that periods of elevated systemic stress coincide with measurable entropy deformation and systematic tail amplification. The results reveal a general instability signature linking entropy structure and extreme-event sensitivity in complex financial systems. Our framework provides a reproducible, analytical, and empirical approach for detecting latent risk amplification and compound extreme-event sensitivity in finite-variance environments.