Saturday, 16 December 2017

statistical mechanics - Motivation for maximum Renyi/Tsallis entropy


The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy. Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy distributions. Is it just because these distributions are heavy tailed?


Is there any motivation (or physical significance) for maximizing Renyi/Tsallis entropies?



Answer



Warning: I do not work in statistical physics, and I therefore do not now if the following has any link with the reason people use Rényi entropies in statistical physics.


John C. Baez wrote a paper (arXiv:1102.2098), stating that the Rényi entropy $H_\beta$ is proportinal to the free energy at temperature defined by $\beta=T_0/T$. This paper is nicely explained on his blog.


The free energy of a system kept at a constant volume and temperature is minimal, and this corresponds, when $T>T_0$ to a maximum Rényi entropy $H_{T/T_0}$.


Edited after reading the paper to correct some mistakes.



No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...