The Fokker–Planck Equation describes the time evolution of probability distributions for stochastic systems. It provides a statistical description complementary to Langevin dynamics. Instead of tracking individual trajectories, the Fokker–Planck equation governs how probabilities change over time. It is widely used to study diffusion, noise-driven systems, and non-equilibrium processes. The equation includes drift and diffusion terms that represent deterministic forces and random fluctuations. Solutions to the Fokker–Planck equation reveal steady states, relaxation behavior, and fluctuation properties. This framework is essential in statistical physics, plasma physics, and chemical kinetics. It also finds applications in finance and population dynamics. The Fokker–Planck equation offers a powerful tool for analyzing complex stochastic behavior in physical systems.
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