  In this paper, we suppose a possible extension of Gibbs ensemble theory so
that it can provide a reasonable description to phase transitions and
spontaneous symmetry breaking. The extension is founded on three hypotheses,
and can be regarded as a microscopic edition of the Landau phenomenological
theory of phase transitions. Within its framework, the state of a system is
determined by the evolution of order parameter with temperature according to
such a principle that the entropy of the system will reach its minimum in this
state. The evolution of order parameter can cause change in representation of
the system Hamiltonian, different phases will realize different
representations. Physically, it turns out that phase transition originates from
the automatic interference among matter waves as temperature is cooled down.
Typical quantum many-body systems are studied with this extended ensemble
theory. In particular, the theory predicts that the specific heat Cp of liquid
He II will vanish linearly as T tends to zero, which is anticipating
experimental verifications.
