Choosing the Friction Parameter

One of the most important features of a numerical method for ergodic dynamics (such as Langevin dynamics) is its preservation of the theoretical global phase space 

The self-diffusion coefficient gives a metric quantifying the diffusion rate. It is often used as a way to compare the rate of phase space exploration between methods, and is typically calculated using the integral of the velocity auto-correlation function. However, in theory one can construct arbitrary methods to artificially scale the velocity auto-correlation function, hence giving inaccurate diffusion constants the momentum sampled may not be the momentum we use to propagate the position with. 

Indeed, calculating the temperature of the system from an average of kinetic energy by 

In a similar way, the speed of exploration of the space should not be determined solely from functions of momentum. Far more reliable is to compute configurational quantities such as barrier crossing rates, passage times to reach some target region of phase space or the diffusion constant through an Einstein relation (which uses the position data). 

Timestep (fs) Timestep (fs) Timestep (fs) Timestep (fs) Timestep (fs) Timestep (fs) 

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