control of unstable steady states by extended time delayed feedback time delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states we present an application of extended time delay autosynchronization introduced by socolar et al phys rev e 50 3245 1994 to an unstable focus this system represents a generic model of an unstable steady state which can be found for instance in hopf bifurcation in addition to the original controller design we investigate effects of control loop latency and a bandpass filter on the domain of control furthermore we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase we present an analysis of the domain of control and support our results by numerical calculations

comparison of maximum entropy and higher order entropy estimators abstract we show that generalized maximum entropy gme is the only estimation method that is consistent with a set of five axioms the gme estimator can be nested using a single parameter into two more general classes of estimators gme estimators each of these gme estimators violates one of the five basic axioms however small sample simulations demonstrate that certain members of these gme classes of estimators may outperform the gme estimation rule

the theory of large deviations from boltzmann s 1877 calculation to equilibrium macrostates in 2d turbulence abstract after presenting some basic ideas in the theory of large deviations this paper applies the theory to a number of problems in statistical mechanics these include deriving the form of the gibbs state for a discrete ideal gas describing probabilistically the phase transition in the curie weiss model of a ferromagnet and deriving variational formulas that describe the equilibrium macrostates in models of two dimensional turbulence a general approach to the large deviation analysis of models in statistical mechanics is also formulated

renyi entropies and fisher informations as measures of nonextensivity in a tsallis setting abstract we study nonextensive statistical scenarios a la tsallis with reference to fisher s information and renyi s entropy a new way of evaluating tsallis generalized expectation values is examined within such a context and is shown to lead to a much better cramer rao bound than the customary procedure a connection between the information measures of fisher s and renyi s is found we show that fisher s measure for translation families remains additive even in a non extensive tsallis setting

escort mean values and the characterization of power law decaying probability densities escort mean values or q moments constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like power laws they naturally appear in the study of many complex dynamical systems particularly those obeying nonextensive statistical mechanics a current generalization of the boltzmann gibbs theory they recover standard mean values or moments for q 1 here we discuss the characterization of a non negative probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities provided that all of them converge this opens the door to a natural extension of the well known characterization for the q 1 instance of a distribution in terms of the standard moments provided that all of them have finite values this question would be specially relevant in connection with probability densities having divergent values for all nonvanishing standard moments higher than a give

expressions for renyi and shannon entropies for bivariate distributions exact forms of renyi and shannon entropies are determined for 27 continuous bivariate distributions including the kotz type distribution truncated normal distribution distributions with normal and centered normal conditionals natural exponential distribution freund s exponential distribution marshall and olkin s exponential distribution exponential mixture distribution arnold and strauss s exponential distribution mckay s gamma distribution distribution with gamma conditionals gamma exponential distribution dirichlet distribution inverted beta distribution distribution with beta conditionals beta stacy distribution cuadras and auge s distribution farlie gumbel morgenstern distribution logistic distribution pearson type vii distribution pearson type ii distribution distribution with cauchy conditionals bilateral pareto distribution muliere and scarsini s pareto distribution distribution with pareto conditionals and the distribution with gumbel conditionals we believe that the results presented here will serve as an important reference for scientists and engineers in many areas

information measures based on tsallis entropy and geometric considerations for thermodynamic systems abstract an analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space we have developed such an analysis for nonextensive thermostatistical frameworks making use of the q divergence derived from tsallis entropy generalized expressions for operator variance and covariance are considered in terms of which the fundamental tensor is given

a simple probabilistic construction yielding generalized entropies and divergences escort distributions and q gaussians abstract we give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution when the parameter of the distribution varies it defines a parametric curve that we call an escort path the renyi divergence appears as a natural by product of the setting we study the dynamics of the fisher information on this path and show in particular that the thermodynamic divergence is proportional to jeffreys divergence next we consider the problem of inferring a distribution on the escort path subject to generalized moment constraints we show that our setting naturally induces a rationale for the minimization of the renyi information divergence then we derive the optimum distribution as a generalized q gaussian distribution

differential escort transformations and the monotonicity of the lmc renyi complexity measure abstract escort distributions have been shown to be very useful in a great variety of fields ranging from information theory nonextensive statistical mechanics till coding theory chaos and multifractals in this work we give the notion and the properties of a novel type of escort density the differential escort densities which have various advantages with respect to the standard ones we highlight the behavior of the differential shannon renyi and tsallis entropies of these distributions then we illustrate their utility to prove the monotonicity property of the lmc renyi complexity measure and to study the behavior of general distributions in the two extreme cases of minimal and very high lmc renyi complexity finally this transformation allows us to obtain the tsallis q exponential densities as the differential escort transformation of the exponential density

information geometry of q gaussian densities and behaviors of solutions to related diffusion equations this paper presents new geometric aspects of the behaviors of solutions to the porous medium equation pme and its associated equation first we discuss thermostatistical structure with information geometry on a manifold of generalized exponential densities a dualistic relation between the two existing formalisms is elucidated next by equipping the manifold of q gaussian densities with such a structure we derive several physically and geometrically interesting properties of the solutions the manifold is proved invariant and attracting for the evolving solutions which play crucial roles in our analysis we demonstrate that the moment conserving projection of a solution coincides with a geodesic curve on the manifold further the evolutional velocities of the second moments and the convergence rate to the manifold are evaluated in terms of the bregman divergence finally we show that the self similar solution is geometrically special in the sense that it is simultaneously geodesic with respect to the mutually dual two affine connections

minimizing thermodynamic length to select intermediate states for free energy calculations and replica exchange simulations in computational thermodynamics a sequence of intermediate states is commonly introduced to connect two equilibrium states we consider two cases where the choice of intermediate states is particularly important minimizing statistical error in free energy difference calculations and maximizing average acceptance probabilities in replica exchange simulations we derive bounds for these quantities in terms of the thermodynamic distance between the intermediates and show that in both cases the intermediates should be chosen as equidistant points along a geodesic connecting the end states

on maximum entropy principle superstatistics power law distribution and renyi parameter abstract the equilibrium distributions of probabilities are derived on the basis of the maximum entropy principle mep for the renyi and tsallis entropies new s forms for the renyi and tsallis distribution functions are found which are normalised with corresponding entropies in contrast to the usual z forms normalised with partition functions z the superstatistics based on the gibbs distribution of energy fluctuations gives rise to a distribution function of the same structure that the renyi and tsallis distributions have the long range tail of the renyi distribution is the power law distribution with the exponent s expressed in terms of the free renyi parameter q as s 1 1 q the condition s 0 gives rise to the requirement q q can be uniquely determined with the use of a further extension of mep as the condition for maximum of the difference between the renyi and boltzmann entropies for the same power law distribution dependent on q it is found that the maximum is realized for q within the range from 0 25 to 0 5 and the exponent s varies from 1 3 to 2 in dependence on parameters of stochastic systems

on the maximum entropy principle and the minimization of the fisher information in tsallis statistics we give a new proof of the theorems on the maximum entropy principle in tsallis statistics that is we show that the q canonical distribution attains the maximum value of the tsallis entropy subject to the constraint on the q expectation value and the q gaussian distribution attains the maximum value of the tsallis entropy subject to the constraint on the q variance as applications of the non negativity of the tsallis relative entropy without using the lagrange multipliers method in addition we define a q fisher information and then prove a q cramer rao inequality that the q gaussian distribution with special q variances attains the minimum value of the q fisher information

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

about closedness by convolution of the tsallis maximizers in this paper we study the stability under convolution of the maximizing distributions of the tsallis entropy under energy constraint called hereafter tsallis distributions these distributions are shown to obey three important properties a stochastic representation property an orthogonal invariance property and a duality property as a consequence of these properties the behaviour of tsallis distributions under convolution is characterized at last a special random convolution called kingman convolution is shown to ensure the stability of tsallis distributions

generalized fisher information matrix in nonextensive systems with spatial correlation by using the q gaussian distribution derived by the maximum entropy method for spatially correlated n unit nonextensive systems we have calculated the generalized fisher information matrix of g ensuremath theta n ensuremath theta m for ensuremath theta 1 ensuremath theta 2 ensuremath theta 3 ensuremath mu q ensuremath sigma q 2 s where ensuremath mu q ensuremath sigma q 2 and s denote the mean variance and degree of spatial correlation respectively for a given entropic index q it has been shown from the cram er rao theorem that 1 an accuracy of an unbiased estimate of ensuremath mu q is improved degraded by a negative positive correlation s 2 that of ensuremath sigma q 2 is worsen with increasing s and 3 that of s is much improved for s ensuremath simeq ensuremath 1 n ensuremath 1 or s ensuremath simeq 1 0 though it is worst at s n ensuremath 2 2 n ensuremath 1 our calculation provides a clear insight to the long standing controversy whether the spatial correlation is beneficial or detrimental to decoding in neuronal ensembles we discuss also a calculation of the q gaussian distribution applying the superstatistics to the langevin model subjected to spatially correlated inputs

persistence of chaos in a time delayed feedback controlled duffing system this paper concerns global phase structures of a time delayed feedback controlled two well duffing system the remains of a global stretch and fold structure along an unstable manifold which develops from an unstable fixed point in function space reveals that the global chaotic dynamics is inherited from the original system by the controlled system the remains of the original chaotic dynamics causes a highly complicated domain of attraction for target orbits and a long chaotic transient before convergence

formulas for renyi information and related measures for univariate distributions in a recent paper song j stat plan infer 93 2001 51 considered renyi information of order and established its connection to the loglikelihood from this relation an intrinsic distribution measure was proposed and analytic expressions of this measure and renyi information were derived for some standard continuous distributions in this paper we derive analytical formulas for renyi and shannon entropies as well as for song s measure for 26 flexible families of univariate continuous distributions we believe that the results presented here will serve as an important reference for scientists and engineers in many areas

on some entropy functionals derived from renyi information divergence we consider the maximum entropy problems associated with renyi q entropy subject to two kinds of constraints on expected values the constraints considered are a constraint on the standard expectation and a constraint on the generalized expectation as encountered in nonextensive statistics the optimum maximum entropy probability distributions which can exhibit a power law behaviour are derived and characterized the renyi entropy of the optimum distributions can be viewed as a function of the constraint this defines two families of entropy functionals in the space of possible expected values general properties of these functionals including nonnegativity minimum convexity are documented their relationships as well as numerical aspects are also discussed finally we work out some specific cases for the reference measure q x and recover in a limit case some well known entropies

towards an information geometric characterization classification of complex systems i use of generalized entropies abstract using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the information geometry based on these entropies our aim at this stage is to construct first some fundamental geometric objects which will be used in the development of our geometrical framework we first establish the existence of a two parameter family of probability distributions then using this family we derive the associated metric and we state a generalized cramer rao inequality this gives a first two parameter classification of complex systems finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes our analysis is based on the two parameter family of generalized entropies of hanel and thurner 2011

publisher s note stationary and dynamical properties of information entropies in nonextensive systems phys rev e 77 031133 2008 we have discussed dynamical properties of the tsallis entropy and the generalized fisher information in nonextensive systems described by the langevin model subjected to additive and multiplicative noise analytical expressions for the timedependent tsallis entropy and generalized fisher information have been obtained with the use of the q moment approach to the fokker planck equation developed in a previous study h hasegawa phys rev e 77 031133 2008 model calculations of the information entropies in response to an applied pulse and sinusoidal inputs have been presented

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

applications of graphical condensation for enumerating matchings and tilings a technique called graphical condensation is used to prove various combinatorial identities among numbers of perfect matchings of planar bipartite graphs and tilings of regions graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph and then re partitioning the united matching actually a multigraph into matchings of two other subgraphs in one of two possible ways this technique can be used to enumerate perfect matchings of a wide variety of planar bipartite graphs applications include domino tilings of aztec diamonds and rectangles diabolo tilings of fortresses plane partitions and transpose complement plane partitions

anomalous diffusion in view of einstein s 1905 theory of brownian motion abstract einstein s theory of brownian motion is revisited in order to formulate a generalized kinetic theory of anomalous diffusion it is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed the fractional derivative naturally appears in the diffusion equation this is the first demonstration of the physical origin of the fractional derivative in marked contrast to the usual phenomenological introduction of it it is also examined if einstein s approach can be generalized to nonlinear kinetic theory to derive a generalization of the porous medium type equation by the appropriate use of the escort distribution

ratios of maximal concurrence parameterized separability functions and generalized peres horodecki conditions the probability that a generic real complex or quaternionic two qubit state is separable can be considered to be the sum of three contributions one is from those states that are absolutely separable that is those which can not be entangled by unitary transformations for which the maximal concurrence over spectral orbits cmax is zero the other two contributions are from the states for which and for which we have previously arxiv 0805 0267 found exact formulas for the absolutely separable contributions in terms of the hilbert schmidt metric over the quantum states and here advance hypotheses as to the exact contributions for a crucial element in understanding the two contributions for cmax 0 is the nature of the ratio r of the cmax parameterized separability function for the complex states to the square of the comparable function for the real states both such functions having clearly displayed jump discontinuities at for the ratio r appears to be of the form 1 kcmax except near while for there is strong numerical evidence that it equals 2 thus according to the dyson index pattern of random matrix theory related phenomena also occur for the minimally degenerate two qubit states and the qubit qutrit states our results have immediate application to the computation of separability probabilities in terms of other metrics such as the bures minimal monotone metric the paper begins with continuous embeddings of the separability probability question in terms of four metrics of interest using generalized peres horodecki conditions

semiclassical information from deformed and escort information measures abstract escort distributions are a well established but for physicists a relatively new concept that is rapidly gaining wide acceptance in world in this work we wish to revisit the concept within the strictures of the celebrated semiclassical husimi distributions hds and thereby investigate the possibility of extracting new semiclassical information contained not in the hd themselves but in their associated escort husimi distributions we will also establish relations for various information measures between their deformed versions j naudts physica a 316 2002 323 and those built up with escort hds bounds on the concomitant power exponents will be determined

notions of the ergodic hierarchy for curved statistical manifolds abstract we present an extension of the ergodic mixing and bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds making use of elements of the information geometry this extension focuses on the notion of statistical independence between the microscopical variables of the system moreover we establish an intimately relationship between statistical models and families of probability distributions belonging to the canonical ensemble which for the case of the quadratic hamiltonian systems provides a closed form for the correlations between the microvariables in terms of the temperature of the heat bath as a power law from this we obtain an information geometric method for studying hamiltonian dynamics in the canonical ensemble we illustrate the results with two examples a pair of interacting harmonic oscillators presenting phase transitions and the 2 2 gaussian ensembles in both examples the scalar curvature results a global indicator of the dynamics

information geometry of generalized bayesian prediction using alpha divergences as loss functions in this paper the methods of information geometry are employed to investigate a generalized bayes rule for prediction taking alpha divergences as the loss functions optimality and asymptotic properties of the generalized bayesian predictive densities are considered we show that the bayesian predictive densities minimize a generalized bayes risk we also find that the asymptotic expansions of the densities are related to the coefficients of the alpha connections of a statistical manifold in addition we discuss the difference between two risk functions of the generalized bayesian predictions based on different priors finally using the non informative priors i e jeffreys and reference priors uniform prior and conjugate prior two examples are presented to illustrate the main results

control of unstable steady states by time delayed feedback methods we show that time delayed feedback methods which have successfully been used to control unstable periodic orbits provide a tool to stabilize unstable steady states we present an analytical investigation of the feedback scheme using the lambert function and discuss effects of both a low pass filter included in the control loop and nonzero latency times associated with the generation and injection of the feedback signal

the enumeration of totally symmetric plane partitions abstract a plane partition is totally symmetric if as an order ideal of n 3 it is invariant under all six permutations of the coordinate axes we prove an explicit product formula for the number of totally symmetric plane partitions that fit in a cube of order n this settles a conjecture published in 1980 by andrews who also attributed it to macdonald and stanley and finishes the program of enumerating plane partitions belonging to each of the 10 symmetry classes proposed by stanley in 1986 as a corollary of the proof we also obtain a new proof of the formula first obtained by mills robbins and rumsey for the number of plane partitions that are invariant under cyclic permutations and transposed complementation

geometrical aspects of a generalized statistical mechanics abstract we discuss here the use of generalized forms of entropy taken as information measures to characterize phase transitions and critical behavior in thermodynamic systems our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models the thermodynamics of the system is the focus of attention in this geometric context

a dual of macmahon s theorem on plane partitions a classical theorem of macmahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula in this paper we present a counterpart of this formula corresponding to the exterior of a concave hexagon obtained by turning 120 after drawing each side macmahon s hexagon is obtained by turning 60 after each step

escort evolutionary game theory abstract a family of replicator like dynamics called the escort replicator dynamic is constructed using information geometric concepts and generalized information divergences from information geometry and statistical thermodynamics a single formula lyapunov function is given that covers the entire class of dynamics which includes the replicator dynamic and the projection dynamic as well as several new dynamics a further class is discussed that allows for more variation such as variable intensities of selection

renyi information measure for a used item recently in the literature a measure of tail heaviness has been proposed based on renyi entropy this measure is very useful in the sense that it can be used to measure tail heaviness even for the distributions for which the kurtosis measure b 2 m 4 m 2 2 does not exist nadarajah and zografos nadarajah zografos information sciences 153 2003 119 138 have derived the expression for this measure for different univariate continuous distributions but this measure can only be used for the lifetime of a new item in case of used item this measure needs some modification in this paper we have modified the measure accordingly so that it can be used in the case of used item and also for the new item we have also derived expressions for this measure for sixteen different univariate distributions and ten other standard distributions derived from the general distributions used in reliability and survival analysis the most of the results obtained in the literature in this direction can be obtained as particular cases of our general results

the other dual of macmahon s theorem on plane partitions abstract in this paper we introduce a counterpart structure to the shamrocks studied in the paper a dual of macmahon s theorem on plane partitions by m ciucu and c krattenthaler 2013 5 which just like the latter can be included at the center of a lattice hexagon on the triangular lattice so that the region obtained from the hexagon by removing it has its number of lozenge tilings given by a simple product formula the new structure called a fern consists of an arbitrary number of equilateral triangles of alternating orientations lined up along a lattice line the shamrock and the fern seem to be the only such connected structures with this property it would be interesting to understand the reason for this

renyi s entropy as an index of diversity in simple stage cluster sampling abstract shannon s measure of entropy and gini simpson s diversity index are usually used by social scientists for measuring diversity of a multinomial population in this paper entropy of order r renyi a 1961 in proceedings of fourth berkeley symposium on mathematics statistics and probability 1 547 561 renyi 1961 is presented as a generalization of shannon s entropy to measure and analyze the diversity asymptotic properties of r order index in a simple stage cluster sampling are investigated also applications to testing hypotheses are discussed finite sample results are computed and to finish a comparison of family members via moments is given

on statistical properties of jizba arimitsu hybrid entropy abstract jizba arimitsu entropy also called hybrid entropy combines axiomatics of renyi and tsallis entropy it has many common properties with them on the other hand some aspects as e g maxent distributions are different in this paper we discuss statistical properties of hybrid entropy we define hybrid entropy for continuous distributions and its relation to discrete entropy additionally definition of hybrid divergence and its connection to fisher metric is also presented interestingly fisher metric connected to hybrid entropy differs from corresponding fisher metrics of renyi and tsallis entropy this motivates us to introduce average hybrid entropy which can be understood as an average between tsallis and renyi entropy

geometry of escort distributions given an original distribution its statistical and probabilistic attributes may be scanned using the associated escort distribution introduced by beck and schlogl and employed in the formulation of nonextensive statistical mechanics here the geometric structure of the one parameter family of the escort distributions is studied based on the kullback leibler divergence and the relevant fisher metric it is shown that the fisher metric is given in terms of the generalized bit variance which measures fluctuations of the crowding index of a multifractal the cramer rao inequality leads to a fundamental limit for the precision of the statistical estimate of the order of the escort distribution we also show quantitatively that it is inappropriate to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics

hilbert schmidt separability probabilities and noninformativity of priors the horodecki family employed the jaynes maximum entropy principle fitting the mean b1 of the bell chsh observable b this model was extended by rajagopal by incorporating the dispersion 2 1 of the observable and by canosa and rossignoli by generalizing the observable b w e further extend the horodecki one parameter model in both these manners obtaining a three parameterb1 2 1 two qubit model for which we find a highly interesting intricate continuum of hilbert schmidt hs separability probabilities in which the golden ratio is featured our model can be contrasted with the three parameterbq 2 q q one of abe and rajagopal which employs a q tsallis parameter rather than and has simply q invariant hs separability probabilities of 1 our results emerge in a study initially focused on embedding certain information metrics over the two level quantum systems into a q framework we find evidence in this regard that srednicki s recently stated biasedness criterion fornoninformative priors yields rankings of priors fully consistent with an information theoretic test of clarke previously applied to quantum systems by slater

the relation between information theory and the differential geometry approach to statistics abstract cencov has shown that the riemannian metric on the probability simplex xi 1 defined by ds 2 dx i 2 x i has an invariance property under certain probabilistically natural mappings no other riemannian metric has the same property the geometry associated with this metric is shown to lead almost automatically to measures of divergence between probability distributions which are associated with kullback bhattacharyya and matusita certain vector fields are associated in a natural way with random variables the integral curves of these vector fields yield the maximum entropy or minimum divergence estimates of probabilities some other consequences of this geometric view are also explored

proof of george andrews s and david robbins s q tspp conjecture the conjecture that the orbit counting generating function for totally symmetric plane partitions can be written as an explicit product formula has been stated independently by george andrews and david robbins around 1983 we present a proof of this long standing conjecture

stability domains for time delay feedback control with latency we generalize a known analytical method for determining the stability of periodic orbits controlled by time delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored we discuss the case of extended time delay autosynchronization and show that nontrivial qualitative features of the domain of control observed in experiments can be explained by taking into account the effects of both the unstable eigenmode and a single stable eigenmode in the floquet theory

some new information measures for fuzzy sets abstract after reviewing some existing measures for fuzzy sets we introduce a new informative measure for discrimination between two fuzzy sets this discriminating measure reduces to the nonprobabilistic entropy of deluca and termini 7 under a special condition the divergence measure between two sets has been defined along with a large set of properties it has also been used to define an ambiguity fuzziness measure renyi s 17 probabilistic entropy of order has been extended to define nonprobabilistic entropy of a fuzzy set various properties of this definition have also been proved applications of these measures to clustering image processing vision etc are highlighted

stationary and dynamical properties of information entropies in nonextensive systems 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 whose result is compared to that obtained by the fpe the cramer rao inequality is shown to be expressed by the extended fisher entropy which is different from the generalized fisher entropy obtained from the generalized kullback leibler divergence in conformity with the tsallis entropy the effect of additive and multiplicative colored noise on information entropies is discussed also