Towards information theory for q-nonextensive statistics without q-deformed distributions |
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| Institution: | 1. School of Surveying and Mapping Engineering, Beijing University of Civil Engineering and Architecture, Beijing 102616, China;2. China National Environmental Monitoring Center, Beijing 100012, China;3. Academy of Disaster Reduction and Emergency Management, MOCA/MOE, Beijing Normal University, Beijing 100875, China;4. State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Science, Beijing 100101, China;5. Department of Geography, University at Buffalo, The State University of New York, Buffalo, NY 14261, United States;6. College of Environment and resource, Fuzhou University, Fuzhou 350116, China |
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| Abstract: | In this paper we extend our recent results P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for systems with embedded self-similarity and q-nonextensivity. We find that this entropy can be uniquely solved in terms of a one-parameter family of information measures. The corresponding entropy maximizer is expressible via a special function known under the name of the Lambert W-function. We analyze the corresponding “high” and “low-temperature” asymptotics and make some remarks on the possible applications. |
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