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  "body": "\n## Summary\n\nThe Langevin equation is a stochastic differential equation for the motion of a particle in a fluid.\nIt combines a deterministic force, a friction force proportional to the velocity, and a random force from collisions with the molecules of the fluid.\nThe friction and the strength of the noise are tied by the temperature, so that the particle reaches thermal equilibrium.\nWithout an external force, the velocity is an [[Ornstein–Uhlenbeck process|HZM2ASCDY4]].\n\n## Explanations\n\n### L1 human\n\nA pollen grain in water is pushed by countless water molecules.\nOn average these pushes slow the grain down, like friction, but they also shake it at random.\nThe Langevin equation is Newton's law with these two extra forces added.\nThe random kicks keep the grain moving, while the friction keeps its speed from growing without bound.\nIn the long run, the velocity of the grain has a normal law whose variance is the temperature divided by the mass, in suitable units.\n",
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