Langevin dynamics

In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems, originally developed by the French physicist Paul Langevin. The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom by the use of .

A molecular system in the real world is unlikely to be present in vacuum. Jostling of solvent or air molecules causes friction, and the occasional high velocity collision will perturb the system. Langevin dynamics attempts to extend molecular dynamics to allow for these effects. Also, Langevin dynamics allows controlling the temperature like a thermostat, thus approximating the canonical ensemble.

Langevin dynamics mimics the viscous aspect of a solvent. It does not fully model an implicit solvent; specifically, the model does not account for the electrostatic screening and also not for the hydrophobic effect. It should also be noted that for denser solvents, hydrodynamic interactions are not captured via Langevin dynamics.

For a system of ${\displaystyle N}$ particles with masses ${\displaystyle M}$, with coordinates ${\displaystyle X=X(t)}$ that constitute a time-dependent random variable, the resulting Langevin equation is

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