The statistical mechanics for an extended nonlinear epigenetic dynamics. I.

An extension of the control equations discussed by Goodwin is proposed which allows for arbitrary strong coupling and for arbitrary parallel coupling of metabolic pools and genetic loci. It is demonstrated that these generalized control equations can be put into canonical form and further that Liouville's theorem applies. In addition, it is demonstrated that after a suitable canonical transformation the resulting partition function can be solved in closed form, and this result, as well as that for the mean energy, is exhibited. Some remarks appropriate to additional extensions are presented.