Dissipation, Chaos, and Timescales: A Timescale-Hierarchical Theory of Near-Integrable Dynamics

We develop a unified theoretical framework relating dissipation, chaos, and timescales in near-integrable Hamiltonian systems. The central claim is that timescale hierarchy, rather than chaos or dissipation taken in isolation, is the primary organizing principle governing long-time dynamics. Chaos is interpreted as a geometrically constrained, timescale-dependent transport mechanism arising from resonance webs and separatrix layers, while dissipation acts as a slow, selective contraction that respects the underlying Hamiltonian skeleton when sufficiently weak. Using explicit inequalities involving Lyapunov times, dissipation times, and spectral gaps, we formulate a regime-based theory that explains long-lived coherence, metastability, and universality in weakly nonconservative systems. The framework challenges standard ergodic and thermodynamic narratives and has implications for celestial mechanics, nonlinear dynamics, plasma physics, and nonequilibrium statistical mechanics.