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A Note on the Connection between Non-Additive Entropy and h-Derivative
Jin-Wen Kang1, Ke-Ming Shen1,2, Ben-Wei Zhang1
1Key Laboratory of Quark & Lepton Physics (MOE), Institute of Particle Physics, Central China Normal University, Wuhan 430079, China.
Entropy (Basel, Switzerland)
|June 28, 2023
Summary
A new generalized entropy form, Sh,h
Area of Science:
- Thermodynamics and Statistical Mechanics
- Non-extensive Systems Analysis
Background:
- Conventional calculus and entropy measures have limitations in describing complex systems.
- Various non-extensive entropy forms exist, but a unified framework is lacking.
Purpose of the Study:
- To introduce a novel two-parameter non-extensive entropic form, Sh,h', that generalizes existing calculus.
- To demonstrate the capability of Sh,h' in describing non-extensive systems.
- To unify and recover various known non-extensive entropic expressions.
Main Methods:
- Introduction of a two-parameter non-extensive entropic form based on the h-derivative.
- Generalization of the Newton-Leibniz calculus framework.
- Analysis of the properties of the generalized entropy form Sh,h'.
Main Results:
- The proposed Sh,h' entropy successfully describes non-extensive systems.
- Sh,h' recovers several well-known entropic expressions, including Tsallis, Abe, Shafee, Kaniadakis, and Boltzmann-Gibbs entropies.
- The properties of this generalized entropy are analyzed.
Conclusions:
- The Sh,h' entropy provides a unified and generalized framework for studying a wide range of entropy measures.
- This new form offers a powerful tool for analyzing complex and non-extensive systems.
- The generalization of calculus through the h-derivative opens new avenues in theoretical physics.
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