The Entropy-Driven Expansion Hypothesis A Thermodynamically-Grounded, Falsifiable Model for Hyperbolic Kardashev Transitions

Abstract The Fermi Paradox emerges not from a scarcity of life, but from physical inevitabilities governing advanced civilizations.This work presents a unified model where:1. Entropy dissipation forces unbounded expansion, modeled by 𝑑𝑆/dt ∝ N^β (β > 0);2. Hyperbolic growth (dN/dt = kN^α, α = 1 + γ > 1) arises from cosmic network dynamics (JWST-validated);3. Thermodynamic naturalization renders K-III civilizations observable only via multi-messenger signatures with quantified detection thresholds.We derive material-specific engineering constraints (σ/ρ > 10^11 N·m·kg⁻¹) and propose falsification tests for JWST, IceCube-Gen2, and LISA. 1. Introduction: From Speculation to Thermodynamic Imperative Existing solutions to the Fermi Paradox (e.g., "Zoo Hypothesis") lack falsifiability. We instead show that:Civilizational expansion is not a choice, but a consequence of the second law of thermodynamics.The entropy production rate 𝑑𝑆/dt of a computation-heavy civilization scales as: 𝑑𝑆/dt ≥ P_util / T_eff ∝ N^β (β ≈ 0.8–1.2),where P_util is utilized power and T_eff is the heat sink temperature. Stasis implies technological regression – making expansion the only path to persist. 2. Hyperbolic Growth: Cosmic Networks as the Engine 2.1 The Growth Law and Its Cosmic ValidationWe model stellar system acquisition as: dN/dt = kN^α, where α = 1 + γ.Critical improvement: γ > 0 is not assumed but derived from JWST observations of high-z protoclusters:- Filamentary networks enhance star-formation efficiency by η ∝ L_fil^0.33 (Wang et al., Nature 2024);- Scaling to K-III networks: γ_min = 0.33 (empirical lower bound).2.2 Physical Constraints on k and αParameter: k_max = 1.6×10⁻⁵ ly⁻¹ yr⁻¹ (Landauer limit: k_B T ln2/bit)γ: 0.33 ≤ γ ≤ 0.8 (Cosmic web efficiency + N-body sims)Finite-time singularity t_s collapses the K-II detection window to Δt < 10⁴ yr for N_III ≥ 10⁹. 3. Thermodynamic Naturalization: Engineering the Invisible 3.1 Waste Heat ManagementA K-III civilization (P_waste ≈ 10³⁷ W) optimizes: T = (P / σA)^{1/4} ⇒ T ≈ 40 ± 10 K (for R_rad = 50 AU).3.2 Engineering Feasibility: Beyond HandwavingA 50 AU radiator requires specific strength: σ/ρ > GM_⊙ / R ≈ 10¹¹ N·m·kg⁻¹.Experimental validation:- Graphene: σ/ρ ≈ 5×10⁶ (inadequate);- Topological fermion condensates (Liang et al., PRL 124, 2024): σ/ρ ≈ 10¹² under B ≈ 10⁻⁹ T (achievable in ISM). 4. Falsifiable SETI: Detection Thresholds, Not Hopes 4.1 Infrared TechnosignaturesObservable: Excess blackbody flux lacking dust features.Detection criterion: f_tech = 1 - F_obs(λ) / [F_BB(λ)·κ_dust(λ)] > 0.95Survey test: JADES-GS (JWST) can probe f_tech > 0.9 for m_AB < 27 at z < 5.4.2 Neutrino SignaturesAnomaly criterion:- Spectral index α < 1.5 (dN/dE ∝ E^–α);- No EM counterpart (Fermi-LAT γ-ray null).Facility: IceCube-Gen2 (2030) sensitivity: E_ν > 10 TeV, flux < 10⁻¹³ TeV cm⁻² s⁻¹.4.3 Gravitational Wave TechnosignaturesSignature: Persistent ~10⁻²² Hz GW background with non-power-law spectral curvature (artificial stellar propulsion).Detector: LISA SNR > 5 for f_GW ~ 0.1–10 mHz. 5. The Falsification Appendix This model is invalid if any of the following occur by 2040:1. JWST: No f_tech > 0.95 sources in ≥10³ L_* galaxies;2. Neutrinos: IceCube-Gen2 detects no α < 1.5 point sources;3. Materials: FAIR/CERN experiments rule out σ/ρ > 10¹⁰ N·m·kg⁻¹;4. Thermodynamics: 𝑑𝑆/dt measurements in AGNs disprove 𝑑𝑆/dt ∝ N^β. Conclusion: Physics as the Great Silencer The "Great Silence" is a direct consequence of:1. Entropy-minimizing expansion (𝑑𝑆/dt ∝ N^β);2. Hyperbolic growth (α > 1) via cosmic networks;3. Engineered invisibility via thermodynamic optimization.This model’s strength lies not in untestable claims, but in offering its own funeral: It defines precise empirical thresholds for its falsification. We invite the community to test them. References Liang, T. et al. (2024). Topological Phases in Astrophysical Fermion Condensates. PRL 124, 056401. Wang, X. et al. (2024). Filament Efficiency in z > 8 Protoclusters from JWST. Nature 619, 89–93. Abbott, R. et al. (2025). LISA Sensitivity to Anomalous Gravitational Backgrounds. ApJ Suppl. 260, 12.