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 stochastic differential equations.
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
where
Here,
If the main objective is to control temperature, care should be exercised to use a small damping constant
The Langevin equation can be reformulated as a Fokker–Planck equation that governs the probability distribution of the random variable X.