A Unified Critical Scaling Theory for Macroscopic Lightning and Quantum Avalanches: From Three-Dimensional Directed Percolation to Testable Predictions

Abstract

Lightning, the most colossal discharge in nature, and flux avalanches in quantum superconductors--phenomena separated by twenty orders of magnitude in scale--display striking fractal similarity. We demonstrate that this is no mere analogy but reveals a deep physical unity. Here, we establish a universal theoretical framework that connects them. By mapping both onto the same three-dimensional reaction-diffusion-advection equation grounded in non-equilibrium statistical physics, we show they belong to the same critical universality class. We demonstrate that both systems belong to the three-dimensional Directed Percolation (3D-DP) universality class near their critical point, sharing a unified set of universal critical exponents (e.g., avalanche size distribution exponent $\tau \approx 1.41$ , fractal dimension $D_f \approx 2.5$). Furthermore, by incorporating the anisotropy and turbulence coupling intrinsic to real thunderstorm environments, we predict novel effects such as anisotropic fractality of lightning channels and the systematic shift of critical exponents by turbulence. The core theoretical breakthrough lies in proposing a geometric correspondence of quantum phase information: through a rigorous mapping, the microscopic quantum phase coherence of superconductors is translated into the curvature and torsion distributions of macroscopic lightning channels, revealing a quantum statistical fingerprint emergent in classical geometry. This framework not only provides a unified paradigm for understanding dissipative structures across scales but also, via seven testable predictions, opens avenues for simulating natural lightning with laboratory quantum systems and developing novel physical early-warning methods.