My question is probably very simple and deals with separation of degrees of freedom in a Monte Carlo Brownian dynamics simulation.
Dealing with a particle in an external potential, I want to simulate a Brownian motion in three spatial dimensions. Is it possible to evaluate the individual degrees of freedom separately i.e. calculate displacement in x, evaluate the probabilities, and accept/reject the step and then repeat for y and z? Or do I have to evaluate all degrees of freedom in a single MC step?
Now what if the degrees of freedom are not independent, i.e. the displacement in x will change the potential (probability) in y etc.? Can the individual degrees of freedom be still calculated separately? Let's say I calculate displacement in x which gets accepted but displacement in y gets rejected. Do I have to throw out both of the displacements? Or can I keep the displacement in x?
I understand that in multi-particle systems, the MC method doesn't evaluate all particles at the same time, therefore it should be possible to evaluate the degrees of freedom separately even if they influence the probability distribution of other degrees of freedom.