Explore the intricacies of extensive entropy functionals and non-ergodic random walks in this 19-minute conference talk presented at GSI. Delve into advanced mathematical concepts and their applications in statistical mechanics and complex systems. Gain insights into the behavior of systems that deviate from traditional ergodic assumptions and understand the role of extensive entropy functionals in describing these phenomena. Examine the implications of non-ergodicity on random walk processes and their relevance in various scientific disciplines.