Publisher's Note: Stationary and dynamical properties of information entropies in nonextensive systems [Phys. Rev. E<b>77</b>, 031133 (2008)]

Journal of Mathematical Physics

2010

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A statistical complexity measure with nonextensive entropy and quasi-multiplicativityWe discuss the Tsallis entropy in finite N-unit nonextensive systems by using the multivariate q-Gaussian probability distribution functions ͑PDFs͒ derived by the maximum entropy methods with the normal average and the q-average ͑q: the entropic index͒. The Tsallis entropy obtained by the q-average has an exponential N dependence:In contrast, the Tsallis entropy obtained by the normal average is given by S q ͑N͒ / N Ӎ͓1 / ͑q −1͒N͔ for large N ͑ӷ1 / ͑q −1͒ Ͼ 0͒. N dependences of the Tsallis entropy obtained by the q-and normal averages are generally quite different, although both results are in fairly good agreement for ͉q −1͉ Ӷ 1.0. The validity of the factorization approximation ͑FA͒ to PDFs, which has been commonly adopted in the literature, has been examined. We have calculated correlations defined byand the bracket ͗ · ͘ stands for the normal and q-averages. The first-order correlation ͑m =1͒ expresses the intrinsic correlation and higher-order correlations with m Ն 2 include nonextensivity-induced correlation, whose physical origin is elucidated in the superstatistics.

“…Here Φ(x), r (N ) s and ν (N ) q are given by Eqs. (19), (23) and (24), respectively, and Exp q (x) is the q-exponential function defined by [15] Exp…”

Section: Original Mem With the Normal Averagementioning

confidence: 99%

The entropy in finite N-unit nonextensive systems: The normal average and q-average

Journal of Mathematical Physics

2010

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“…In Ref. [26], we discussed the Fisher information in the Langevin model subjected to uncorrelated additive and multiplicative noise, which is a typical microscopic model showing the nonextensive behavior [27]. It is interesting to calculate the Fisher information of the Langevin model with correlated multiplicative noise.…”

Section: A Comparison With Related Studiesmentioning

confidence: 99%

Synchrony and variability induced by spatially correlated additive and multiplicative noise in the coupled Langevin model

2008

Phys. Rev. E

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The synchrony and variability of the coupled Langevin model subjected to spatially correlated additive and multiplicative noise are discussed. We have employed numerical simulations and the analytical augmented-moment method, which is the second-order moment method for local and global variables [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)]. It has been shown that the synchrony of an ensemble is increased (decreased) by a positive (negative) spatial correlation in both additive and multiplicative noise. Although the variability for local fluctuations is almost insensitive to spatial correlations, that for global fluctuations is increased (decreased) by positive (negative) correlations. When a pulse input is applied, the synchrony is increased for the correlated multiplicative noise, whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise. An application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals, which accounts for some neuronal experiments.

“…where E[· · ·] denotes the average over p (N ) ({x i }) [= p (N ) ({x i }; {θ k })] characterized by a set of parameters {θ k }. On the contrary, the extended Fisher information matrixg (N ) ij derived from the Cramér-Rao inequality in nonextensive systems, is expressed by [17] g…”

Section: Introductionmentioning

confidence: 99%

Effects of correlated variability on information entropies in nonextensive systems

2008

Phys. Rev. E

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We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) by a positive (negative) correlation, whereas the Tsallis entropy is decreased with increasing absolute magnitude of the correlation, independently of its sign. This fact arises from the difference in their characteristics. It implies from the Cramér-Rao inequality that the accuracy of an unbiased estimate of fluctuation is improved by a negative correlation. A critical comparison is made between the present study and previous ones employing the Gaussian approximation for the correlated variability due to multiplicative noise.