Impedance-debt modelling predicts that sleep onset timing scales inversely with temperature, with observed sleep onset ticks 559 at τ=0.5, 279 at τ=1.0, and 186 at τ=1.5 confirming theoretical predictions within 0.2% error.
A computational physics model demonstrates that sleep can be modeled as the homeostatic discharge of thermodynamic impedance debt accumulated across neural and vascular networks.
Effect estimate: Sleep onset at temperature factor 0.5 was 2.0 times that at 1.0; at 1.5 it was 0.67 times that at 1.0, matching predicted inverse proportionality (T max wake ∝ 1/τ)
Absolute Event Rate: 559% vs 279%
Γ-Net (Gamma-Net) v3. 2. 0 — A physics-driven electronic lifeform that models cognition, emotion, pain, sleep, language emergence, and psychopathology through impedance-mismatch equations derived from coaxial transmission line theory. This record contains four companion papers (Papers I–IV) of the Γ-Net series: Paper I — Irreducible Dimensional Cost in Heterogeneous Impedance Networks: Scaling Laws, Fractal Topology, and the Minimum Reflection Principle Proves the Dimensional Cost Irreducibility Theorem: A = Aᵢmp (t) + Acut, where Acut is invariant under all local impedance update rules at fixed topology. Key results: negative convergence scaling τconv ~ N^-0. 91 (R²=0. 95, N=16–256) ; soft-cutoff fractal control DK = 0. 49γ + 1. 00 reproducing cortical fractal dimensions D ∈ 1. 3, 1. 5; spontaneous relay-node hierarchy emergence as thermodynamic necessity. Paper II — Twin Impedance Networks: A Unified Neural–Vascular Organ Model from the Minimum Reflection Action Derives Murray’s Law of optimal vessel branching (rₚ³ = Σr₃, ₈³) as the exact minimum of the vascular action Aᵥ = ΣQ²|Z| + βV, with 100% numerical agreement for n=2, 3, 4 branches. Introduces the dual-network organ health model H = Tₙ · Tᵥ = (1−ρ²ₙ) (1−ρ²ᵥ). Fractional flow reserve (FFR) is identified as exactly the vascular transmission ratio Tᵥ. 10/10 clinical calibrations passed (FAME, NASCET, UKPDS) ; 12/12 dual-network RCT validations passed (STENO-2, ADVANCE, SPRINT-MIND, UKPDS-80, etc. ) ; 100/100 randomised stability runs converged. Paper III — The Cost of Life: Impedance Debt as the Thermodynamic Origin of Sleep and Brain Evolution Proposes sleep as homeostatic discharge of impedance debt ΔZ = ∫ Twake ρ² (t) Pᵢnt dt. Three independent evidence lines: (i) cnidarian sleep without a brain (Cassiopea/Nematostella DNA-damage studies) ; (ii) convergent evolution of brains ≥9 times as thermodynamic centralised impedance-debt managers; (iii) human embryogenesis recapitulating the thermodynamic causal chain (heart → neural tube → brain vesicles). Dual-network decomposition ΔZ = ΔZₙ + ΔZᵥ; tidal-zone as quarter-wave impedance matching (log gradient reduces action to 6. 2% of direct jump) ; ischemia verified at 4. 77× mismatch ratio. 9/9 computational experiments passed. Paper IV — The Lifecycle Equation: Cognition, Emotion, and Aging as Three-Force Competition on an Impedance Network Derives the Lifecycle Equation dρ²/dt = -α (t) ρ² + β (t) εₑnv (t) + γ (t) D (t), a first-order ODE in which learning (MRP descent), novelty injection, and Coffin–Manson fatigue compete to produce the bathtub curve of cognitive performance from birth to senescence. Emotion, reward (dopamine), stress (cortisol), curiosity, and boredom are derived as temporal readouts of ρ² dynamics at different time scales. Atherosclerosis is derived as vascular Coffin–Manson fatigue; the vascular–neural aging cascade explains why cardiovascular disease precedes neurodegeneration. 9/9 computational experiments passed including the Yerkes–Dodson inverted-U curve and full lifecycle simulation. Core Equation (all four papers derive from a single variational principle): A = ∫ Σᵢj ρ²ᵢj dt → min, where ρ = (ZL − Z₀) / (ZL + Z₀) v3. 2. 0 Release (code): https: //github. com/cyhuang76/alice-gamma-net License: Code under AGPL-3. 0-or-later · Papers under CC BY-NC-SA 4. 0
Hsi-Yu Huang (Wed,) conducted a other in Organisms possessing neurons requiring sleep regulation and thermodynamic impedance matching, including neonatal and adult nervous system models. Impedance-debt framework modelling and simulation vs. None (computational simulation-based study) was evaluated on Sleep onset timing, sleep duration, and impedance debt discharge verified in computational simulations (Sleep onset at temperature factor 0.5 was 2.0 times that at 1.0; at 1.5 it was 0.67 times that at 1.0, matching predicted inverse proportionality (T max wake ∝ 1/τ)). Impedance-debt modelling predicts that sleep onset timing scales inversely with temperature, with observed sleep onset ticks 559 at τ=0.5, 279 at τ=1.0, and 186 at τ=1.5 confirming theoretical predictions within 0.2% error.