arXiv 1211.21242012-11-09cond-mat.stat-mech

对“强关联系统的大偏差理论”一文的答复

Reply to Comment on "Towards a large deviation theory for strongly correlated systems"

Guiomar Ruiz, Constantino Tsallis

备注：: 8 pages, 5 figures, reply to comment
DOI：: 10.1016/j.physleta.2012.12.009

摘要：

该文件是由Touchette评论包含一个计算研究打开了大门，一个理想的推广标准大偏差理论（适用于一组$N$几乎独立的随机变量）系统属于一个特殊的，但无处不在，类强相关性。它集中在三个相互关联的方面，即（i）我们表现出强有力的数值迹象表明，标准的指数概率律是渐近取代幂律作为其主导项的大$N$;（ii）次显性项似乎与遵循$q$-统计的系统的典型的$q$-指数行为一致，从而加强了$q$-指数的指数的广义熵性质，基本上是$N$乘以$q$-广义速率函数;（iii）我们所关注的强相关性类对应于中心极限定理意义下的吸引子，其为$Q$-高斯分布（原则上$1 < Q < 3$），其与（对称）Lévy分布相关地不同，唯一的例外是Cauchy-Lorentz分布（其对应于$Q = 2$），其中它们一致，如众所周知的。在他的评论中，Touchette同意讨论第（i）点，但不幸的是，第（ii）和（iii）点，正如我们在这里详细介绍的那样，显然逃脱了他的分析。因此，他的结论声称没有特殊的联系与$q$-指数是不合理的。

英文摘要：

The paper that is commented by Touchette contains a computational study which opens the door to a desirable generalization of the standard large deviation theory (applicable to a set of $N$ nearly independent random variables) to systems belonging to a special, though ubiquitous, class of strong correlations. It focuses on three inter-related aspects, namely (i) we exhibit strong numerical indications which suggest that the standard exponential probability law is asymptotically replaced by a power-law as its dominant term for large $N$; (ii) the subdominant term appears to be consistent with the $q$-exponential behavior typical of systems following $q$-statistics, thus reinforcing the thermodynamically extensive entropic nature of the exponent of the $q$-exponential, basically $N$ times the $q$-generalized rate function; (iii) the class of strong correlations that we have focused on corresponds to attractors in the sense of the Central Limit Theorem which are $Q$-Gaussian distributions (in principle $1 < Q < 3$), which relevantly differ from (symmetric) Lévy distributions, with the unique exception of Cauchy-Lorentz distributions (which correspond to $Q = 2$), where they coincide, as well known. In his Comment, Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) have, as we detail here, visibly escaped to his analysis. Consequently, his conclusion claiming the absence of special connection with $q$-exponentials is unjustified.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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