Extended Ensemble Theory, Spontaneous Symmetry Breaking, and Phase   Transitions
  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. 
Ming-wen Xiao