Distributions and channel capacities in generalized statistical mechanics |
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| Affiliation: | 1. Faculty of Mathematics, University of Southampton, Southampton SO17 1BJ, UK;2. Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BZ, UK;1. Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Lisboa, Portugal;2. Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Gothenburg, Sweden;3. Departamento de Matemática e Aplicações, Universidade do Minho, Guimarães, Portugal;4. Centro de Matemática, Universidade do Minho, Braga, Portugal;1. Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;2. Department of Physics, Pukyong National University, Busan 608-737, Republic of Korea;1. School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China;2. School of Physics and Optoelectronic Technology, Taiyuan University of Technology, Taiyuan 030024, China;1. Meteorological Research Institute, Tsukuba Ibaraki 305-0052, Japan;2. Meteorological Satellite Center, Kiyose Tokyo 204-0012, Japan |
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| Abstract: | The purpose of this note is twofold. Firstly, we consider generalizations of Shannon's entropy and its applications to thermodynamics based on extensivity considerations. Secondly, we apply the generalized entropy formalism to deriving various generalised channel capacities. We arrive at some surprising conclusions of systems achieving “super-capacitance” or “sub-capacitance” depending on the circumstances. These results suggest the possibility of improving the conventional Shannon capacity by using physical systems obeying more generalized statistics, but also predict behaviour which is hard to reconcile with experience. |
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