Brief Review on the Connection between the Micro-Canonical Ensemble and the S-Canonical Probability Distribution

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Non-extensive Statistical Mechanics

Background:

• Generalizations of Boltzmann-Gibbs entropy are actively researched.
• Sq non-additive entropies form a prominent framework within these generalizations.
• Sq-based thermostatistics presents unique characteristics compared to other entropy generalizations.

Purpose of the Study:

• To review the connection between Sq-canonical distributions and the micro-canonical ensemble.
• To focus on micro-canonical scenarios that lead to Sq-canonical distributions.
• To examine historical and recent works on this Sq-micro-canonical connection.

Main Methods:

• Review of existing literature on thermostatistics and entropy generalizations.
• Analysis of micro-canonical ensemble scenarios.
• Identification and discussion of Sq-canonical distributions within these scenarios.

Main Results:

• The close connection between Sq-canonical distributions and the micro-canonical ensemble is a key feature of Sq-based thermostatistics.
• This connection has been explored in various directions since its initial identification.
• Sq-canonical distributions have been implicitly present in historical works and explicitly investigated in recent research.

Conclusions:

• The Sq-micro-canonical connection is a significant aspect of generalized thermostatistics.
• Understanding this link provides deeper insights into non-standard statistical mechanics.
• Further research can build upon these findings to explore new applications.