A well-known class of biophysical models, first introduced by Kerner, is shown to admit a convenient Hamiltonian formulation in which motion through the phase space of system variables involves explicit constraints. To treat the macroscopic properties of such models, we develop an ensemble theory of systems subjected to phase space constraints. For such systems we obtain a generalized Hamiltonian statistical mechanics which preserves much of the structure and efficacy of the corresponding physical theory. In a first application of the method, we recover Kerner's original biological ensemble as a special case involving information optimality and conservative biosystems.