yeah, that would tend to keep the dynamo pretty much upright all the time. It's dynamics law, no need for thermodynamics here. I don't think the whole problem involves any statistical mechanics here, just very complicated navier-stokes + heat generation and transfer + current loops. Probably as bad as plasma dynamics, and the PDE have solutions that are extremely sensitive to initial conditions, yet the stable dynamo is an attractor and all the chaos stuff that was trendy 15 years ago and everybody's jaded.

Pierre