Non-Shannonian Inference Procedure and Thermostatistics

Abstract

Power-law distributions or more generally non-exponential distributions are ubiquitous in nature and observed in many diverse scientific disciplines, indicating a high degree of complexity and self-organization of the system under scrutiny. The entropic understanding of these distributions is one possible approach which combines Statistical Thermodynamics and Information Theory by virtue of the inference procedure called Maximum Entropy Principle (MaxEnt). In the last thirty years the former inference recipe has found numerous applications in various fields of research. Despite, however, all these applications, there are unsolved fundamental issues which weaken the validity of this approach, such as the physical origin of the correlation parameters, non-conformity of non-Shannonian entropies to the Shore-Johnson axioms, arbitrariness of the averaging procedure, etc. My research interest in this field is to build a solid theoretical foundation which will tell us where and under what conditions we can use these concepts.

Author: Thomas Oikonomou

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