New statistical models of nonergodic cognitive systems and their pathologies

Cognition most singularly involves choice that reduces uncertainty. Reduction of uncertainty implies the existence of an information source 'dual' to the cognitive process under study. However, information source uncertainty for path-dependent nonergodic systems cannot be described as a conventional Shannon 'entropy' since time averages are not ensemble averages. Nonetheless, the essential nature of information as a form of free energy allows study of nonergodic cognitive systems having complex dynamic topologies whose algebraic expression is in terms of directed homotopy groupoids rather than groups. This permits a significant extension of the Data Rate Theorem linking control and information theories via an analog to the spontaneous symmetry breaking arguments fundamental to modern physics. In addition, the identification of information as a form of free energy enables construction of dynamic empirical Onsager models in the gradient of a classic entropy that can be built from the Legendre transform of even path-dependent information source uncertainties. The methodology provides new analytic tools that should prove useful in understanding failure modes and their dynamics across a broad spectrum of cognitive phenomena, ranging from physiological processes at different scales and levels of organization to critical system automata and institutional economics.