On Thermodynamic Information
| Autor: | Miao, Bing, Qian, Hong, Wu, Yong-Shi |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 \phi is employed as an analytic "device" to express information as statistical dependency contained in the topological sub-\sigma-algebra structure. Via thermo-doubling, Fenchel-Young equality (FYE) that consists of \phi(x) and its conjugate \psi(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 \phi(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. Comment: 20 pages |
| Databáze: | arXiv |
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