  An approach is developed, combining the ideas of quantum statistical
mechanics and multichannel theory of scattering, for treating statistical
systems whose constituents can possess different bound states realized as
compact clusters. The main principles for constructing multichannel cluster
Hamiltonians are formulated: principle of statistical correctness, principle of
cluster coexistence, and principle of potential scaling. The importance of the
principle of statistical correctness is emphasized by showing that when it does
not hold the behaviour of thermodynamic functions becomes essentially
distorted. And moreover, unphysical instabilities can appear. The ideas are
carefully illustrated by a statistical model of hot nuclear matter.
