system dynamics

Ergodic theory: invariant measures and mixing

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The ergodic theory opens fascinating perspectives beyond the traditional boundaries of mathematics and physics. This discipline focuses on the study of dynamical systems and how, over time, the trajectories of a system explore its entire state space. In particular, the key concepts of invariant measures, mixing, and ergodicity provide essential tools for understanding how seemingly … Read more

Out-of-equilibrium systems: self-organizing structures

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Remote thermodynamic equilibrium systems reveal a fascinating facet of nature, where apparent disorder becomes the breeding ground for a new organization. Contrary to the classical idea that entropy inevitably progresses towards chaos, these systems exhibit a paradoxical phenomenon where irreversibility is the engine of order, giving rise to self-organized structures capable of maintaining dynamical stability. … Read more