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We have calculated the Tsallis entropy and Fisher information matrix(entropy) of spatially-correlated nonextensive systems, by using an analyticnon-Gaussian distribution obtained by the maximum entropy method. Effects ofthe correlated variability on the Fisher information matrix are shown to bedifferent from those on the Tsallis entropy. The Fisher information isincreased (decreased) by a positive (negative) correlation, whereas the Tsallisentropy is decreased with increasing an absolute magnitude of the correlationindependently of its sign. This fact arises from the difference in theircharacteristics. It implies from the Cram\'{e}r-Rao inequality that theaccuracy of unbiased estimate of fluctuation is improved by the negativecorrelation. A critical comparison is made between the present study andprevious ones employing the Gaussian approximation for the correlatedvariability due to multiplicative noise.

Effects of correlated variability on information entropies in nonextensive systems