On the Validity of the Master Equation for Finite Closed Systems

Abstract

Two equations for the macroscopic part W of the statistical operator are considered: 1. the master equation Ẇ = − MW, 2. the exact equation Ẇ = − [FORMULA OMITTED] K(t − τ) W(τ) dτ. It follows from the physical equivalence of the solutions together with a stability assumption and the assumption that there is a time τ* after which also the derivatives of the solutions are equivalent, that τ* is the life-time of the kernel K and that M = [FORMULA OMITTED] K(τ) dr. Conversely, the equivalence of the solutions follows from assumptions on the life-time of the kernel K together with a stability assumption and a smoothness assumption on the initial statistical operator W(0). © 1978, Walter de Gruyter. All rights reserved.