Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution united? How to unite? In this paper starting out from nonequilibrium entropy evolution equation we proved that a new entropy decrease could spontaneously emerge in nonequilibrium system with internal attractive interaction. This new entropy decrease coexists with the traditional law of entropy increase, both of them countervail each other, so that the total entropy of isolated system can be able to decrease. It not only makes isolated system but also helps open system to produce self-organizing structure. We first derived a statistical formula for this new entropy decrease rate, and compared it both in mathematical form and in microscopic physical foundation with the statistical formula for the law of entropy increase which was derived by us some years ago. Furthermore, we gave the formulas for the time rate of change of total entropy in isolated system and open system. The former is equal to the sum of the formula for the law of entropy increase and the formula for the new entropy decrease rate, the latter is the algebraic sum of the formulas for entropy increase, entropy decrease and entropy flow. All of them manifest the unity of thermodynamic degradation and self-organizing evolution. As the application of the new theoretical formulas, we discussed qualitatively the emergency of inhomogeneous structure in two real isolated systems including clarifying the inference about the heat death of the universe.