  We show that both information erasure process and trace process can be
realized by projective measurement. And a partial trace operation consists to a
projective measurement on a subsystem. We show that a nonunitary operation will
destroy the wave-behavior of a particle. We give a quantum manifestation of
Maxwell's demon and give a quantum manifestation of the second law of
therodynamics. We show that, considering the law of memontum-energy
conversation, the evolution of a closed system should be unitary and the von
Neumann entropy of the closed quantum system should be least.
