Mathematical Foundations of Nonextensive Statistical Mechanics

10.1142/12499 ◽  
2022 ◽  
Author(s):  
Sabir Umarov ◽  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Nonextensive Statistical Mechanics ◽  
Mathematical Foundations

Laws of large numbers for q-dependent random variables and nonextensive statistical mechanics

2017 ◽  
Vol 31 (15) ◽  
pp. 1750117
Author(s):  
Marco A. S. Trindade
Keyword(s):  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Nonextensive Statistical Mechanics ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers

In this work, we prove a weak law and a strong law of large numbers through the concept of [Formula: see text]-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

scholarly journals Nondistributive algebraic structures derived from nonextensive statistical mechanics

2008 ◽  
Vol 49 (9) ◽  
pp. 093509 ◽  
Author(s):  
Pedro G. S. Cardoso ◽  
Ernesto P. Borges ◽  
Thierry C. P. Lobão ◽  
Suani T. R. Pinho
Keyword(s):  
Statistical Mechanics ◽  
Algebraic Structures ◽  
Nonextensive Statistical Mechanics
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