Cyclic Dynamics, Recurrence, and Structural Persistence in Irreversible Systems

Cyclic behavior is ubiquitous across physical, biological, informational, and cognitive systems, appearing in phenomena ranging from oscillatory dynamics and biological rhythms to ecological and astrophysical cycles. This ubiquity presents an apparent paradox: how can cyclic organization persist in a universe governed by irreversible entropy increase? This work develops a non-equilibrium framework demonstrating that cyclic dynamics emerge as stable attractors within dissipative systems, while exact recurrence is generically forbidden by entropy production and environmental coupling. The analysis distinguishes local cyclicity from global irreversibility and identifies structural and informational constraints—not microscopic states—as the elements that persist across cycles.