# Interacting system and relaxation times

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 but here is a kick - I THINK that S2 is changing 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?

-