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Beyond Boltzmann-Gibbs-Shannon in Physics and Elsewhere
Constantino Tsallis1,2,3
1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems-Rua Dr. Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Generalized statistical mechanics using nonadditive entropies addresses complex systems where Boltzmann-Gibbs (BG) theory fails. This approach offers new insights into quantum mechanics, networks, and thermodynamics.
Area of Science:
- Theoretical Physics
- Statistical Mechanics
- Complex Systems
Background:
- Classical mechanics, electromagnetism, relativity, quantum mechanics, and Boltzmann-Gibbs (BG) statistical mechanics are foundational to physics.
- BG statistical mechanics excels in simple systems but shows limitations in complex systems, including quantum phenomena (black holes) and information theory (image/time series processing).
- Complex systems often exhibit long-range correlations, long memory, and scale-free networks, indicating a need for generalized theories.
Purpose of the Study:
- To review the generalization of BG statistical mechanics using nonadditive entropies.
- To explore the predictions, verifications, and applications of these generalized theories.
- To highlight successful applications across diverse scientific fields.
Main Methods:
- Review of theoretical frameworks generalizing Boltzmann-Gibbs statistical mechanics.
- Analysis of nonadditive entropies and their mathematical properties.
- Examination of empirical evidence and case studies from various scientific domains.
Main Results:
- Nonadditive entropies provide a successful generalization of BG theory for complex systems.
- These generalized approaches have demonstrated efficacy in diverse areas like quantum information, high- and low-energy physics, nonlinear dynamics, and network science.
- Applications include modeling earthquakes, turbulence, long-range interacting systems, and scale-free networks.
Conclusions:
- Generalized statistical mechanics with nonadditive entropies is crucial for understanding complex systems.
- This framework offers a unified approach to phenomena previously unexplained by classical BG theory.
- The review underscores the broad applicability and predictive power of these advanced statistical methods.
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