Abstract
Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of Wang (EPJB, 2002) and use the incomplete information theory to retrieve the Tsallis entropy. We change the incomplete information axioms to consider the escort probability and obtain a correct form of Tsallis entropy in comparison with Wang’s work.
Highlights
IntroductionThe entropy is the key concept to extract universal features of a system from its microscopic details
The entropy is the key concept to extract universal features of a system from its microscopic details.In the statistical mechanics two forms are considered to describe the concept of entropy
Using simple algebraic manipulation which can be found in every textbooks of statistical mechanics, the equality between these two definitions is proved
Summary
The entropy is the key concept to extract universal features of a system from its microscopic details. Shannon derived the same form for the entropy which is similar to the Gibbs relation He used the axioms of the information theory that are intuitively correct for non-interacting systems in physics [2]. The existence of long range interaction between system’s entities fails the condition of non-interacting components for a system when we want to derive the BGS entropy In this case simulations show that the entropy and energy are non-extensive [11,12]. There are many natural or social systems with small size or long range interaction between their components, we can use the non-extensive statistical mechanics to study such systems. The third section is devoted to introducing the escort probability and derivation of Tsallis entropy from axioms of the incomplete information theory. We summarize our work and discuss its advantages and disadvantages
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