Unifying Classical Paradoxes with Energy-Efficiency Theory: Identity, Quantum Measurement, and the Nature of Time

From the Ship of Theseus to Schrödinger's cat, from Zeno's arrow to Maxwell's demon, classical paradoxes have persistently challenged our understanding of identity, measurement, time, and information. Despite their diversity, these paradoxes share a common root: the implicit assumption that existence can be characterized by static snapshots (material constitution, geometric position, or information state) rather than by dynamical processes. Energy-Efficiency Theory (EET) offers a unified ontological framework based on three causal-functional postulates. We introduce the core concepts of constrained energy density U(r), Yang's energy ratio η = Ė_resp/Ė_main, inertial inheritance, and the real/observed space distinction. Using these tools, we provide systematic resolutions to: (i) identity paradoxes (Ship of Theseus, Replication, Swampman, Twin Earth) by grounding identity in the continuity of energy-allocation trajectories; (ii) quantum paradoxes (Schrödinger's cat, Maxwell's demon) by showing that macroscopic systems have η ≪ 1, suppressing coherence, and that information has an energetic cost; (iii) motion paradoxes (Zeno's arrow) by invoking a minimal time interval Δt_min = d_min/v_max. The framework not only resolves each paradox individually but also reveals their common underlying structure: each arises from conflating ontological energy processes with their rule-layer