A new entropy based on a group-theoretical structure

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• 作者：Evaldo M.F. Curado^a ; ^b ; ^{evaldo@cbpf.br" class="auth_mail" title="E-mail the corresponding author} ; Piergiulio Tempesta^c ; ^d ; ^{p.tempesta@fis.ucm.es" class="auth_mail" title="E-mail the corresponding author} ; ^{piergiulio.tempesta@icmat.es" class="auth_mail" title="E-mail the corresponding author} ; Constantino Tsallis^a ; ^b ; ^e ; ^{tsallis@cbpf.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized entropies ; Group theory ; Statistical mechanics
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：366
• 期：Complete
• 页码：22-31
• 全文大小：400 K

文摘

A multi-parametric version of the nonadditive entropy S_q$S_q$ is introduced. This new entropic form, denoted by S_a,b,r$S_{a,b,r}$, possesses many interesting statistical properties, and it reduces to the entropy S_q$S_q$ for b=0$b=0$, a=r:=1−q$a=r:=1-q$ (hence Boltzmann–Gibbs entropy S_BG$S_{BG}$ for b=0$b=0$, a=r→0$a=r\to 0$). The construction of the entropy S_a,b,r$S_{a,b,r}$ is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of S_a,b,r$S_{a,b,r}$ with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy S_a,b,r$S_{a,b,r}$ can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles N$N$ of the system, or even stabilizes, by increasing N$N$, to a limiting value.

This paves the way to the use of this entropy in contexts where the size of the phase space does not increase as fast as the number of its constituting particles (or subsystems) increases.