Mathematical formulation

When trying to model molecular processes, one often comes against the problem of how to compensate between scales. On one hand, there is the fact that observable phenomena occur at the macroscopic scale, and so often times we average out the interactions to get a general equation for our appropriate scale. On the other hand, the microscopic interactions can and do perform interactions with each other. The result is that the deterministic macroscale approximation fails when interactions occur around the area of a phase transition or bifurcation point due to fluctuations.