Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations (opens in new tab)

arXiv:2603.01278v1 Announce Type: new Abstract: Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation, starting from the growth law $dy/dx = y^q$. By identifying the $q$-logarithm as the natural coordinate system of the state space, we construct a thermodynamic framework where the drift term remains linear in the probab...