Comments On The Algorithm
The key property of the KMC algorithm (and of the FRM one) is that if the rates are correct, if the processes associated with the rates are of the Poisson process type, and if different processes are independent (i.e. not correlated) then the KMC algorithm gives the correct time scale for the evolution of the simulated system.
If furthermore the transitions follow detailed balance, the KMC algorithm can be used to simulate thermodynamic equilibrium. However, KMC is widely used to simulate non-equilibrium processes (Meng 1994), in which case detailed balance need not be obeyed.
The KMC algorithm is efficient in the sense that every iteration is guaranteed to produce a transition. However, in the form presented above it requires operations for each transition, which is not too efficient. In many cases this can be much improved on by binning the same kinds of transitions into bins, and/or forming a tree data structure of the events. A constant-time scaling algorithm of this type has recently been developed and tested in (Slepoy 2008).
The major disadvantage with KMC is that all possible rates and reactions have to be known in advance. The method itself can do nothing about predicting them.
Read more about this topic: Kinetic Monte Carlo
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