New exponential, logarithm and q-probability in the non-extensive statistical physics
Won Sang Chung
TL;DR
This paper introduces new exponential and logarithm functions based on q-sum and q-product, explores q-mapping from probability to q-probability, and demonstrates q-additivity of q-entropy in non-extensive statistical physics.
Contribution
It proposes novel exponential and logarithm functions satisfying distributivity and introduces a q-mapping framework for probability in non-extensive physics.
Findings
New q-exponential and q-logarithm functions satisfying distributivity.
Q-entropy is shown to be q-additive.
Framework for q-mapping from probability to q-probability.
Abstract
In this paper, a new exponential and logarithm related to the non-extensive statistical physics is proposed by using the q-sum and q-product which satisfy the distributivity. And we discuss the q-mapping from an ordinary probability to q-probability. The q-entropy defined by the idea of q-probability is shown to be q-additive.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Mathematical Theories and Applications · Benford’s Law and Fraud Detection