Overdamped Limit of Langevin Dynamics

An interesting special case of Langevin dynamics is obtained by considering the large y limit, often referred to as the overdamped limit. In cases where the friction constant is scaled by the inverse mass (so y is replaced by yM in (6.32)-(6.33)) such as in [233], this is instead known as the zero-mass limit. In this model the inertial dynamics is assumed to be dominated by collisional effects. Let v = M p and assume that the acceleration is negligible, so that Langevin dynamics reduces to 

This is also sometimes referred to as Brownian dynamics or Smoluchowski dynamics. The transition from Langevin to Brownian dynamics is typically referred to as the Kramers to Smoluchowski limit.  

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