Temporal organization in living systems: toward a physics of life

Abstract Classical dynamical systems theory is based on asymptotic stability assumptions. This approach has long dominated theoretical biology, providing insight into stability and functional organization. Yet, living systems rarely converge to static attractors; rather, they adapt continuously and exhibit structural plasticity. We examine the limitations of purely asymptotic descriptions and consider extensions such as metastability and chronotaxicity. We argue that temporal organization provides a useful perspective for understanding living systems and examine how chronotaxicity offers a mathematical description of systems where function and stability can emerge from the maintenance of timing relationships across scales through mutual coupling. This synthesis points toward the development of a broader physics of living systems that integrates non-equilibrium and non-autonomous dynamics with measurable coordination invariants, while providing a basis for both theoretical formalization and the extraction of biologically relevant information from time-series data.