1. It is based on the Generalized Langevin Equation ( GLE ). 2. On small timescales, inertial effects are prevalent in the Langevin equation . 3. In physics, however, stochastic integrals occur as the solutions of Langevin equations . 4. However, the Langevin equation is more general. 5. On long timescales, the mathematical Brownian motion is well described by a Langevin equation . 6. In those cases, the Langevin equation , which looks at particle acceleration, must be used. 7. The equipartition theorem can be used to derive the Brownian motion of a particle from the Langevin equation . 8. The " Langevin equation " describes advection, diffusion, and other phenomena in an explicitly stochastic way. 9. In 1991, he derived, with Bedeaux, the Langevin equation for a Brownian particle using only causality and time reversal invariance. 10. In the white noise setting described so far, the quantum Langevin equation for an arbitrary system operator a takes a simpler form:
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