We derive the classic Yerkes-Dodson effect of applied stress on real-world performance in a highly natural manner from fundamental assumptions on cognition and its dynamics, as constrained by the asymptotic limit theorems of information and control theories. We further examine how differences in an underlying cognitive probability model might associate with different expressions of psychopathology. Vulnerability to psychopathology is framed as a ratio of toxic stress in the context of ‘noise’ and uncertainty to resilience. A ‘thin tailed’ underlying distribution appears to characterize expression of ‘ordinary’ situational depression/anxiety symptoms induced by stress, while a ‘fat tailed’ underlying distribution appears to be associated with brain structure and function abnormalities leading to serious mental illness where symptoms are not only emerging in the setting of severe stress but may emerge in a highly punctuated manner at relatively lower levels of stress. A simple hierarchical optimization model explores the effects of environmental ‘shadow price’ constraints in buffering or aggravating the effects of stress. Extension of the underlying theory to other patterns of pathology, like immune disorders and premature aging, seems apt. Ultimately, the probability models studied here can be converted to new statistical tools for the analysis of observational and experimental data.