This study investigates accelerated physical–chemical processes in a complex adaptive surface-engineered system represented by a nano-multilayer TiAlCrSiYN/TiAlCrN PVD coating under the extreme tribological conditions of ultra-high-performance dry machining of hardened H 13 tool steel. These processes are similar to the different catalyzing phenomena. Experimental results of tool life vs. wear rate, SEM/TEM data of the worn surfaces, XPS and EDS data of tribo-films formed on the friction surfaces, and chip surface morphology are presented in this study. The corresponding relationships between self-organization, self-organized criticality, and various catalyzing phenomena were evaluated on the basis of the accrued data. A method of enhancing these processes through the variation of machining conditions is also outlined, which resulted in the improvement of coated tool life by 35%.