Titre : The winding path to entropy 

Auteurs : Constantino Tsallis,  

Revue : Entropy: Thermodynamics – Energy – Environment – Economy  

Numéro : Special issue LILA 

Volume : 4 

Date : 2023/05/30 

DOI : 10.21494/ISTE.OP.2023.0985 

ISSN : 2634-1476 

Résumé : The concept of entropy has traveled along winding roads since it was introduced in 1865 by Clausius as a key piece to complete thermodynamics and its Legendre transforms structure. Boltzmann, followed by Gibbs, has then revealed its microscopic interpretation, thus leading to the additive expression $$$S_{BG}=k\sum_{i=1}^W p_i \ln (1/p_i)$$$. A few decades later von Neumann provided its quantum form, and Shannon connected it to the theory of communications. Some time later, in 1961, Rényi generalized the Boltzmann-Gibbs-von Neumann-Shannon form, though preserving its additivity. There was then a real explosion of nonadditive entropic functionals, close to fifty nowadays. Inspired by multifractals, we postulated in 1988 the form $$$S_q\equiv k \sum_{i=1}^W p_i \ln_q (1/p_i)$$$ [with $$$\ln_q z \equiv (z^{1-q}-1)/(1-q);\, \ln_1z=\ln z$$$] as a basis for generalizing the Boltzmann-Gibbs statistical mechanics itself. Along the present brief perspective, we present the foundations and main applications of this theory, currently referred to as nonextensive statistical mechanics. 

Éditeur : ISTE OpenScience