A Hexalogy

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

• [arXiv: 2603.21391]
  
  

PartII: Trinity of Varentropy: Finiteness, Fluctuations, and Stability in Power-Law Statistics

• [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

• [arXiv: 2603.01273]
  
  

PartVI: Breakdown of Perturbative Expansions and Exact Algebraic Absorption of Finite-Size Fluctuations in Statistical Mechanics

• [arXiv: 2603.22358]