Nonadditive Entropies and Statistical Mechanics at the Edge of Chaos - Cornerstones

Explore a comprehensive lecture on nonadditive entropies and statistical mechanics at the edge of chaos. Delve into key concepts such as Boltzmann-Gibbs entropy, Q-logarithm, additivity, and extensivity. Examine the historical context with references to Einstein, Planck, and Gibbs. Investigate the Central Limit Theorem, Logistic Map, and Standard Map. Analyze the Second Principle of Thermodynamics and the validity and failure of the Boltzmann Weight. Discover applications in complex networks and high-energy physics. Gain insights into cornerstone principles that shape our understanding of statistical mechanics and entropy in complex systems.

Intro
Nonadditive entropies
Boltzmann Gibbs entropy
Q logarithm
Is sq unique
ABE 2000
Einstein 1910
Additivity and extensivity
Nonzero probability equally probable events
Summary
Why
Planck 1900
Gibbs 1902
Qproduct
Central Limit Theorem
Index Q
Logistic Map
Standard Map
Gaussian
Second Principle of Thermodynamics
Validity Failure of the Boltzmann Weight
Xy Model
Boltzmann Factor
French Experiment
High energy example
Complex networks