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Langevin equation

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In physics, a Langevin equation is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Langevin equation typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast (microscopic) variables are responsible for the stochastic nature of the Langevin equation. One application is to Brownian motion, which models the fluctuating motion of a small particle in a fluid.

This plot corresponds to solutions of the complete Langevin equation obtained using the Euler–Maruyama method. The left panel shows the time evolution of the phase portrait of a harmonic oscillator at different temperatures. The right panel captures the corresponding equilibrium probability distributions. At zero temperature, the velocity rapidly decays from its initial value (the red dot) to zero due to damping. For nonzero temperatures, the velocity can be kicked to values higher than the initial value due to thermal fluctuations. At long times, the velocity remains nonzero, and the position and velocity distributions correspond to that of thermal equilibrium.

Paul Langevin

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Paul Langevin was a French physicist who developed Langevin dynamics and the Langevin equation. He was one of the founders of the Comité de vigilance des intellectuels antifascistes, an anti-fascist organization created after the 6 February 1934 far right riots. Being a public opponent of fascism in the 1930s resulted in his arrest and being held under house arrest by the Vichy government for most of World War II. Langevin was also president of the Human Rights League (LDH) from 1944 to 1946, having recently joined the French Communist Party.

Paul Langevin

Albert Einstein, Paul Ehrenfest, Paul Langevin, Heike Kamerlingh Onnes, and Pierre Weiss at Ehrenfest's home in Leiden in the Netherlands