Tier 1 #21: Statistical Mechanics in the Information-Theoretic Unification framework — quantum statistics, fluctuation theorems, information, and complex systems

This paper formulates statistical mechanics — classical, quantum, non-equilibrium, fluctuation, informational, and complex-systems statistical mechanics — entirely inside the Information-Theoretic Unification (ITU) framework. Across eight phases (143-150), we (i) reconstruct Boltzmann/Maxwell-Boltzmann/Gibbs equilibrium statistics as the Kₛtat substructure of ITU; (ii) cover Fermi-Dirac / Bose-Einstein quantum statistics, BEC at TBEC ≈ 170 nK for Rb-87, and Fermi degeneracy producing the Chandrasekhar mass 1. 4 Mₛun; (iii) demonstrate phase transitions, critical exponents, universality classes, and Wilson's renormalization group with Onsager's exact 2D Ising Tc = 2. 269 J/kB reproduced via Monte Carlo; (iv) develop non-equilibrium thermodynamics via Onsager reciprocity, Kubo linear response, and the fluctuation-dissipation theorem, verified against Einstein D = mu*kB*T for Brownian motion; (v) prove Jarzynski's equality ⟨exp (-beta W) ⟩ = exp (-beta Delta F) and Crooks' fluctuation theorem in a harmonic-spring switching simulation, and verify the Landauer limit Wₑrase >= kB T ln 2 = 17. 9 meV/bit at 300 K; (vi) establish the Kₛtat ↔ Kᵢnfo isomorphism through Shannon entropy, Jaynes max-entropy, and von Neumann entropy (including Bell-state maximal entanglement S = ln 2) ; (vii) analyze active matter (Vicsek model), self-organized criticality (BTW sandpile τ ≈ 1. 18), Barabási-Albert scale-free networks (gamma ≈ 2. 73), Turing patterns (Gray-Scott), and the thermodynamics of life (human ATP turnover ≈ 100 W). Phase 150 integrates these into a 21-vertex ITU polytope in which #21 Statistical Mechanics attains the new maximum degree 20, alongside the other four Block A papers. The construction establishes the UNIVERSAL FOUNDATION Kgeom ⊕ Kcosmic ⊕ Kfield ⊕ Kₛtat, completing physics inside a four-K-state architecture, and yields 10 falsifiable predictions (Pₐvg = 0. 635; 5 strong, 4 medium, 1 weak) for 2026-2050. Block A paper 5/9, Pass-1 milestone 68. 2% (Phase 150/220). Companion archive contains eight reproducible Python simulations and their figures and JSON summaries. Tier 0 concept DOI: 10. 5281/zenodo. 20109209. Tier 0 v3. 0: 10. 5281/zenodo. 20200156. Block A prior: #17 QG (10. 5281/zenodo. 20230667), #18 BH (10. 5281/zenodo. 20233070), #19 Cosmology (10. 5281/zenodo. 20233952), #20 SM (10. 5281/zenodo. 20234703).