The Dominant Term Positivity of Time-Evolution Operator in the Physical Representation

Abstract

In the diagonal subspace of the Liapounov representation introduced by the Brussels group, the dominant terms for any matrix element of the time evolution operator are given explicitly if the Hamiltonian satisfies some general conditions held in all models studied so far. All these expressions have semi-definite positive forms so that, when they are different from zero for a particular isolated system, the “microscopic entropy” will increase monotonically until the system approaches the well-known microcanonical equilibrium.