Langevin Equation
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High Quality Content by WIKIPEDIA articles!In statistical physics, a Langevin equation is a stochastic differential equation describing the time evolution of a subset of the degrees of freedom. The diagram at right shows a phase portrait of the time evolution of the momentum, p = mv, vs. position, r of a harmonic oscillator. Deterministic motion would follow along the ellipsoidal trajectories which cannot cross each other without changing energy. The presence of a molecular fluid environment (represented by diffusion and damping terms) continually adds and removes kinetic energy from the syste...
High Quality Content by WIKIPEDIA articles!In statistical physics, a Langevin equation is a stochastic differential equation describing the time evolution of a subset of the degrees of freedom. The diagram at right shows a phase portrait of the time evolution of the momentum, p = mv, vs. position, r of a harmonic oscillator. Deterministic motion would follow along the ellipsoidal trajectories which cannot cross each other without changing energy. The presence of a molecular fluid environment (represented by diffusion and damping terms) continually adds and removes kinetic energy from the system, causing an initial ensemble of stochastic oscillators (dotted circles) to spread out, eventually reaching thermal equilibrium.
