A Hexalogy will appear in 2026.
The equations speak for themselves.
Foundations (Probability Theory, Statistical Physics, Information Geometry):
PartI: A Constructive Approach to q-Gaussian Distributions: α-Divergence as Rate Function and Generalized de Moivre-Laplace Theorem
PartII: Trinity of Varentropy: Finiteness, Fluctuations, and Stability in Power-Law Statistics
Physica A: Statistical Mechanics and its Applications (2026), in press. [arXiv: 2603.27997]
PartIII:
[arXiv: xxxx.xxxxx] (Link to be updated; expected in 2026)
Applications (Nonlinear Dynamics, Quantum Fluids, Complex Systems):
PartIV: Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations
Physical Review E 113, 064118 (2026). [DOI: 10.1103/r6y7-ffqs][arXiv: 2603.01278]
PartV: Exact Density Profiles of 1D Quantum Fluids in the Thomas-Fermi Limit: Geometric Hierarchy to the Tonks-Girardeau Gas
PartVI: Breakdown of Perturbative Expansions and Exact Algebraic Absorption of Finite-Size Fluctuations in Statistical Mechanics
Physica A: Statistical Mechanics and its Applications 699, 131903 (2026). [DOI: 10.1016/j.physa.2026.131903][arXiv: 2603.22358]