  The Tsallis entropy and Fisher information entropy (matrix) are very
important quantities expressing information measures in nonextensive systems.
Stationary and dynamical properties of the information entropies have been
investigated in the $N$-unit coupled Langevin model subjected to additive and
multiplicative white noise, which is one of typical nonextensive systems. We
have made detailed, analytical and numerical study on the dependence of the
stationary-state entropies on additive and multiplicative noise, external
inputs, couplings and number of constitutive elements ($N$). By solving the
Fokker-Planck equation (FPE) by both the proposed analytical scheme and the
partial difference-equation method, transient responses of the information
entropies to an input signal and an external force have been investigated. We
have calculated the information entropies also with the use of the probability
distribution derived by the maximum-entropy method (MEM), whose result is
compared to that obtained by the FPE. The Cram\'{e}r-Rao inequality is shown to
be expressed by the {\it extended} Fisher entropy, which is different from the
{\it generalized} Fisher entropy obtained from the generalized Kullback-Leibler
divergence in conformity with the Tsallis entropy. The effect of additive and
multiplicative {\it colored} noise on information entropies is discussed also.
