Correspondences between Neural Network Operations and Statistical Physics

This document systematically catalogs formal correspondences between neural network operations and statistical physics, classifying each by evidential strength: algebraic identity, structural isomorphism, or approximate equivalence. It covers foundational results (Shannon, Landauer, Jaynes), empirical scaling laws, mean-field theory of deep learning, information thermodynamics, optimal transport in generative models, and emerging physical computing substrates - including coherent Ising machines, probabilistic bits, memristive in-memory computing, and thermodynamic processors. For each correspondence, primary sources are cited with explicit scope-of-applicability constraints, maintaining a consistent distinction between mathematical formalism and engineering advantage. The compilation serves as a reference framework for assessing where physics-informed approaches to computation rest on proven theorems versus empirical analogies. Available in Russian (concepts_ru.pdf) and English (concepts_en.pdf).