Nonextensive Entropy, Prior PDFs and Spontaneous Symmetry Breaking

The entropy in finite $N$-unit nonextensive systems: the ordinary average and $q$-average

We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the $q$-average ($q$: the entropic index). The Tsallis entropy obtained by the $q$-average has an exponential $N$ dependence: $S_q^{(N)}/N \simeq \:e^{(1-q)N \:S_1^{(1)}} $ for large $N$ ($\gg \frac{1}{(1-q)} >0$). In contrast, the Tsallis entropy obtained by the normal average is given by $S_q^{(N)}/N \simeq [1/(q-1)N]$ for large $N$ ($\gg \frac{1}{(q-1)} > 0)$. $N$ dep…