The Principle of Minimum Time: A Unifying Constraint from Energy-Efficiency Theory

Yang's Minimum Time Principle Δt_min = d_min / v_max is derived as a theorem from the three causal-functional postulates of Energy-Efficiency Theory (EET). The derivation is direct: any physically resolvable change requires a signal to propagate across a minimal spatial scale d_min at a maximum speed v_max. We operationalize d_min as d_min ≡ ħ v_max / E_b, where E_b is the constraint barrier, thereby unifying the spatial and energetic limits. The principle is cross-scale universal. Key applications include: (i) a first-principles derivation of the Debye frequency ω_D = π v_s / a in solids, where the lattice constant a emerges from the balance between maintenance power Ė_main and thermal energy k_B T; (ii) a physical resolution of Zeno's paradox in which infinite temporal divisibility drives the energy ratio η = Ė_resp / Ė_main ≫ 1, forcing a thermodynamic reset analogous to the Sisyphus cycle; and (iii) the emergence of the Planck time t_Pl = √(ħG/c^5) as the coincidence of quantum and gravitational constraints, demonstrating EET's compatibility with established physics. The framework distinguishes real space (continuous ontological unfolding) from observed space (projection through measurement). The minimum time is the fundamental resolution limit of observed space. A falsifiable prediction for quantum gate operations is given, including a critical crossover scale L* = ħ v_max / E_b where the dominant bottleneck switches from geometric signaling (observed space) to thermodynamic maintenance (real space). The paper clarifies the background-independent nature of the spatial parameter L, provides a graph-theoretic definition of topological distance, and conjectures a quantitative relation between shared constraint barriers and entanglement entropy: E_b,shared ∝ S_ent · k_B T_eff.