2023/12/06 by Bing Miao, Hong Qian, Miao, Bing +3 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2312.03454
openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Information based thermodynamic logic is revisited. It consists of two parts: Part A applies the modern theory of probability in which an arbitrary convex function ϕis employed as an analytic "device" to express information as statistical dependency contained in the topological sub-σ-algebra structure. Via thermo-doubling, Fenchel-Young equality (FYE) that consists of ϕ(x) and its conjugate ψ(y) establishes the notion of equilibrium between x and y through duality symmetry and the principle of maximum entropy/minimum free energy. Part B deals with a given set of repetitive measurements, where an inherent convex function emerges via the mathematics of large deviations. Logarithm-based Shannon entropy with ϕ(x)=-log x figures prominently for i.i.d. sample statistics. Information can be a measure of the agreement between a statistical observation and its theoretical models. Maximum likelihood principle arises here and FYE provides a thermodynamic energetic narrative of recurrent data.