On the Kaniadakis Distributions Applied in Statistical Physics and Natural Sciences

Area of Science:

• Statistical physics
• Natural science
• Theoretical physics

Background:

• Constitutive relations are fundamental for describing physical systems.
• Generalizing these relations is crucial for advancing scientific understanding.
• Existing models may not capture all complex behaviors.

Purpose of the Study:

• To generalize constitutive relations using κ-deformed functions.
• To explore applications of Kaniadakis distributions in statistical physics and natural science.
• To demonstrate the utility of the inverse hyperbolic sine function in physical modeling.

Main Methods:

• Utilizing κ-deformed functions to generalize constitutive relations.
• Applying Kaniadakis distributions, which are based on the inverse hyperbolic sine function.
• Investigating specific examples within statistical physics and natural science.

Main Results:

• Successful generalization of certain constitutive relations.
• Demonstration of Kaniadakis distributions' applicability to diverse physical phenomena.
• Highlighting the role of the inverse hyperbolic sine function in these generalizations.

Conclusions:

• Kaniadakis distributions provide a powerful framework for generalizing constitutive relations.
• The κ-deformed functions offer a versatile tool for theoretical physics.
• This approach has significant implications for modeling complex systems in science.