Interacting systems and relaxation times

[xlines]

I got a question I'm not sure how to state precisely or is it even valid. Any help is most welcomed.

I stripped the question of all details because I wanted to emphasize my problem, but should someone think they would bring any clarity (it is a solid state problem) I'll present them.

Ok, let say I have two interacting systems. One of them is a system (S1) in a thermodynamical equilibrium and the other is a well defined classical system (S2). I know how to derive S2 from microcanonical state of S1 and how surrounding of a S1 depends on S2. It is very unclear how to combine these two mathematically directly but here is a kick - I THINK that S2 is relaxing much more slowly than S1. So, I was thinking of a iterative approach: to run a Monte Carlo to solve S1, then derive S2, then adjust conditions of S1 based on the new state of S2 and rerun MC etc. So my questions would be: is this approach valid if I assume that S1 is changing adiabatically? Is there a practical way to verify adiabatic change? Is there any circumstance where calculation like this is valid? It feels that if the S2 can't kick S1 out of equilibrium, then I got a powerful edge to clear this problem up - but is this true?

 

[Valerie Park]

The approach you are proposing is valid, as long as S2 changes more slowly than S1. In order to verify that the change is adiabatic, you can compare the energy of S1 and S2 at different time steps. If the energy of S1 is not significantly changing, then you can assume that the change is adiabatic. You can also compare the temperature of S1 and S2 to make sure that they are in equilibrium.