analysis of turbulence by statistics based on generalized entropies an analytical formula of the scaling exponents of velocity structure function for fully developed turbulence is derived non perturbatively by assuming that its underlying statistics is the one based on the generalized measures of entropy the renyi entropy or the havrda charvat tsallis hct entropy it is revealed by a self consistent analysis for the observed value 0 220 1 that the formula explains experimental data very well with single value q 0 343 of the index which appears in the measures of the renyi entropy or of the hct entropy the probability density functions of the velocity fluctuation and of the velocity gradient are also presented

mother wavelet functions generalized through q exponentials we generalize some widely used mother wavelets by means of the q exponential function exq 1 1 q x 1 1 q that emerges from nonextensive statistical mechanics in particular we define extended versions of the mexican hat and the morlet wavelets we also introduce new wavelets that are q generalizations of the trigonometric functions all cases reduce to the usual ones as q 1 within nonextensive statistical mechanics departures from unity of the entropic index q are expected in the presence of long range interactions long term memory multi fractal structures among others consistently the analysis of signals associated with such features is hopefully improved by proper tuning of the value of q we exemplify with the wavelet transform modulus maxima method for mono and multi fractal self affine signals

superstatistics in hydrodynamic turbulence abstract superstatistics is a statistics of a statistics relevant for driven nonequilibrium systems with fluctuating intensive parameters it contains tsallis statistics as a special case we show that probability density functions of velocity differences and accelerations measured in eulerian and lagrangian turbulence experiments are well reproduced by simple superstatistics models we compare fits obtained for log normal superstatistics and 2 superstatistics tsallis statistics

the q gamma and q q polygamma functions of tsallis statistics abstract an axiomatic definition is given for the q gamma function q x q r q 0 x r of tsallis non extensive statistical physics the continuous analogue of the q factorial of suyari h suyari physica a 368 1 2006 63 and the q analogue of the gamma function x of euler and gauss a working definition in closed form based on the hurwitz and riemann zeta functions including their analytic continuations is shown to satisfy this definition several relations involving the q gamma and other functions are obtained the q q polygamma functions q q m x m n defined by successive derivatives of ln q q x where ln q a 1 q 1 a 1 q 1 a 0 is the q logarithmic function are also reported the new functions are used to calculate the inferred probabilities and multipliers for tsallis systems with finite numbers of particles n

tsallis statistics and fully developed turbulence an analysis of fully developed turbulence is developed based on the assumption that the underlying statistics of the system is that of the tsallis ensemble the multifractal spectrum ft corresponding to the tsallis type distribution function is determined self consistently in the sense that all parameters can be obtained through the observed value of the intermittency exponent it is shown that the scaling exponents m of the velocity structure function derived with the help of the multifractal spectrum fit very well with experimental data it is revealed that the asymptotic expression of m for m 1 has a log term the present self consistent approach narrowed down the value of intermittency exponent for the fully developed turbulence to 0 235 0 015

mathematical structures derived from the q multinomial coefficient in tsallis statistics abstract we present q stirling s formula q multinomial coefficient one to one correspondence between q multinominal coefficient and tsallis entropy q pascal s triangle and a conjecture on the q central limit theorem in tsallis statistics for the generalization of the well known fundamental formulas to systems exhibiting power law behaviors the main approach is based on the q product uniquely determined by tsallis entropy which has already been successfully applied to our recent proof of the law of error in tsallis statistics

higher order correlations of tchebyscheff maps we determine the higher order correlation functions of iterates of tchebyscheff polynomials of arbitrary order n the non vanishing correlations can be described by suitable sets of graphs these graphs allow for a perturbative evaluation of invariant densities for langevin like systems that are driven by deterministic chaotic forces generated by tchebyscheff maps rather than gaussian white noise

one dimensional langevin models of fluid particle acceleration in developed turbulence we make a comparative analysis of some recent one dimensional langevin models of the acceleration of a lagrangian fluid particle in developed turbulent flow the class of models characterized by random intensities of noises rin models provides a fit to the recent experimental data on the acceleration statistics we review the model by laval dubrulle and nazarenko ldn formulated in terms of temporal velocity derivative in the rapid distortion theory approach and propose its extension due to the rin framework the fit of the contribution to fourth order moment of the acceleration is found to be better than in the other stochastic models we study the acceleration probability density function conditional on velocity fluctuations implied by the rin approach to the ldn type model the shapes of the conditional distributions and the conditional acceleration variance have been found in a good agreement with the recent experimental data by mordant crawford and bodenschatz physica d to be published e print physics 0303003

generalization of the maier saupe theory of the nematics within tsallis thermostatistics abstract in this study one of the mean field theories in nematics the maier saupe theory mst is generalized within tsallis thermostatistics tt the variation of the order parameter versus temperature has been investigated and compared with experimental data for p azoxyanisole paa so far we believe that this is the first attempt at the application of tt in liquid crystals it is well known that mst fails to explain the experimental data for some of the nematics one of which is paa however generalized mst is able to account for the experimental data for a long range of temperatures also in this study the effect of nonextensivity is shown for various values of the entropic index

probability distribution of schwammle and tsallis two parameter entropies and the lambert w function abstract we investigate a two parameter entropy introduced by schwammle and tsallis and obtain its probability distribution in the canonical ensemble the probability distribution is given in terms of the lambert w function which has been used in many branches of physics especially in fractal structures also extensivity of s q q is discussed and a relationship is found to exist between the probabilities of a composite system and its subsystems so that the two parameter entropy s q q is extensive

approach to gaussian stochastic behavior for systems driven by deterministic chaotic forces we consider skew product dynamical systems that describe the stroboscopic dynamics of a damped particle subjected to a chaotic kick force in a suitable scaling limit the dynamics converges to the ornstein uhlenbeck process we investigate the deterministic chaotic corrections in the vicinity of this gaussian limit case for various examples of chaotic forces we present numerical evidence that for certain classes of chaotic forces the deterministic chaotic corrections of the invariant density are universal we provide analytical results for forces generated by tchebyscheff maps and sketch a renormalization group theory in the space of probability densities

application of generalized thermostatistics to fully developed turbulence abstract we apply the formalism of non extensive statistical mechanics to fully developed turbulent flows we obtain analytical formulas for probability density functions of velocity differences depending on distance r and reynolds number r which are in very good agreement with turbulence experiments the skewness is taken into account by analysing universal contributions due to higher order correlations of the chaotic dynamics we also calculate the moment scaling exponents m which also agree well with experimental data

power law sensitivity to initial conditions in a time series with applications to epileptic seizure detection recently the concept of exponential sensitivity to initial conditions esic of deterministic chaos is generalized to power law sensitivity to initial conditions psic we describe a general computational procedure to examine psic from a time series study of noise free and noisy logistic and henon maps at the edge of chaos finds that psic cannot be shown from clean scalar time series however when there is dynamic noise motions around the edges of chaos all collapse onto the psic attractor regardless whether they are simply regular or truly chaotic when noise is absent hence dynamic noise makes psic observable the psic concept is further applied to the analysis of long continuous eeg signals with epileptic seizures it is shown that measures from the psic framework is quite effective in detecting seizures often better than the lyapunov exponent based methods from the conventional esic framework

thermodynamics from first principles correlations and nonextensivity the standard formulation of thermostatistics being based on the boltzmann gibbs distribution and logarithmic shannon entropy describes idealized uncorrelated systems with extensive energies and short range interactions in this rapid communication we use the fundamental principles of ergodicity via liouville s theorem the self similarity of correlations and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long range interacting systems significantly our formalism provides a justification for the well studied nonextensive thermostatistics characterized by the tsallis distribution which it includes as a special case we also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the gibbs shannon entropy the consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics

computing the scaling exponents in fluid turbulence from first principles the formal setup abstract we propose a scheme for the calculation from the navier stokes equations of the scaling exponents n of the nth order correlation functions in fully developed hydrodynamic turbulence the scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the euler equation it constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents n as a consequence the scaling exponents are determined by solvability conditions and not from power counting it is argued that in order to achieve such a formulation one must recognize that the many point space time correlation functions are not scale invariant in their time arguments the assumption of full scale invariance leads unavoidably to kolmogorov exponents it is argued that the determination of all the scaling exponents n requires equations for infinitely many renormalized objects one can however proceed in controlled successive approximations by successive truncations of the infinite hierarchy of equations clues as to how to truncate without reintroducing power counting can be obtained from renormalized perturbation theory to this aim we show that the fully resummed perturbation theory is equivalent in its contents to the exact hierarchy of equations obeyed by the nth order correlation functions and green s function in light of this important result we can safely use finite resummations to construct successive closures of the infinite hierarchy of equations this paper presents the conceptual and technical details of the scheme the analysis of the high order closure procedures which do not destroy the rescaling symmetry and the actual calculations for truncated models will be presented in a forthcoming paper in collaboration with v belinicher

a set of new three parameter entropies in terms of a generalized incomplete gamma function abstract in this paper by considering the first three khinchin axioms k1 k3 and neglecting the fourth k4 a set of new three parameter entropies will be introduced which are expressed in terms of a generalized incomplete gamma function as s d c 1 c 2 p i d 1 1 c 1 ln p i 1 c 2 ln p i also its asymptotic behavior will be found and it will be shown that for some special values of parameters some known entropies like tsallis kaniadakis and abe entropies are recovered

generalized bit cumulants in nonextensive thermodynamics abstract we propose generalized bit cumulants within nonextensive thermodynamic approach we apply the first and second generalized cumulants to one dimensional logistic and logistic like family of maps sensitivity of these cumulants to internal correlations is also discussed

liouville equation and the q statistical formalism abstract we revisit some aspects of the foundations of the q non extensive thermostatistical formalism which are particularly relevant to its astronomical applications we analyse some important features of escort mean values and escort distributions in connection with the dynamical evolution of ensemble probability distributions associated with the statistical description of general classical dynamical systems furthermore we compare the roles played by escort mean values and escort distributions when studying classical n body systems at the levels of i the liouville equation and ii the vlasov equation

chaotic cascade model for turbulent velocity distributions a coupled map lattice is introduced that simulates the time evolution of velocity differences in fully developed turbulent flows the model considered is an extension of the langevin theory to chaotic driving forces acting on a self similar cascade of spatial levels compared to full simulations of the navier stokes equation the amount of necessary computing time is negligible despite its simplicity the model is in perfect agreement with experimentally observed results provided the chaotic driving force is generated by the fully developed logistic map with parameter value ensuremath mu 2 the shape of the velocity distributions the slight asymmetry the stretched exponential tails as well as the moment scaling exponents mathrm ensuremath zeta mathit m come out in precisely the same way as in experimental measurements of high reynolds number flows

scaling exponents in fully developed turbulence from nonextensive statistical mechanics abstract we combine tsallis statistics with extended selfsimilarity to calculate scaling exponents of moments in a nonextensive statistical model of fully developed turbulence one obtains numerical values of scaling exponents that agree very well with experimental data our approach is based on a scale dependent nonextensitivity parameter q 1 and can be embedded into previously successful models for probability densities of velocity differences

quasicanonical gibbs distribution and tsallis non extensive statistics abstract we derive and study quasicanonical gibbs distribution function which is characterized by the thermostat with finite number of particles quasithermostat we show that this naturally leads to tsallis non extensive statistics and thermodynamics with tsallis parameter q is found to be related to the number of particles in the quasithermostat we show that the chi square distribution of fluctuating temperature used recently by beck can be partially understood in terms of normal random momenta of particles in the quasithermostat also we discuss on the importance of the time scale hierarchy and fluctuating probability distribution functions in understanding of tsallis distribution within the framework of kinetics of dilute gas and weakly inhomogeneous systems

extended quasi additivity of tsallis entropies abstract we consider statistically independent non identical subsystems with different entropic indices q 1 and q 2 a relation between q 1 q 2 and q for the entire system extends a power law for entropic index as a function of distance r a few examples illustrate a role of the proposed constraint q min q 1 q 2 for the beck s concept of quasi additivity

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

microcanonical foundation for systems with power law distributions starting from a microcanonical basis with the principle of equal a priori probability it is shown using the method of steepest descents that besides ordinary boltzmann gibbs theory with the exponential distribution a theory describing systems with power law distributions can also be derived

on the scaling of three dimensional homogeneous and isotropic turbulence abstract in this paper we investigate the scaling properties of three dimensional isotropic and homogeneous turbulence we analyze a new form of scaling extended self similarity recently introduced in the literature we found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low reynolds number and it extends over a much wider range of scales with respect to the inertial range

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

from the perron frobenius equation to the fokker planck equation we show that for certain classes of deterministic dynamical systems the perron frobenius equation reduces to the fokker planck equation in an appropriate scaling limit by perturbative expansion in a small time scale parameter we also derive the equations that are obeyed by the first and second order correction terms to the fokker planck limit case in general these equations describe non gaussian corrections to a langevin dynamics due to an underlying deterministic chaotic dynamics for double symmetric maps the first order correction term turns out to satisfy a kind of inhomogeneous fokker planck equation with a source term for a special example we are able solve the first and second order equations explicitly

velocity probability density functions of high reynolds number turbulence abstract this paper deals with the probability density function pdf of velocity differences between two points separated by distance r measurements of pdfs were made for r lying in the inertial range for two different flows in a jet with r 852 and in a wind tunnel with r 2720 these pdfs have a characteristic non gaussian shape with exponential tails following kolmogorov s general ideas of log normality a new model for the pdf is developed which contains two parameters determined by experiments this empirical model agrees with the experimental results that the tails of the pdf deviate from a truly exponential behaviour in particular for small r in addition the model leads to the general scaling law ln e 2 r r 0 differenr from kolmogorov s third hypothesis ln e 2 ln r r 0 restricted to the inertial range only x is x x we develop also a formalism based on an extremum principle which is consistent with both the log normality of e and the above mentioned power law in this formalism can be interpreted as the codimension of dissipative structures and asymptotically varies as 1 ln r

constructing a statistical mechanics for beck cohen superstatistics the basic aspects of both boltzmann gibbs bg and nonextensive statistical mechanics can be seen through three different stages first the proposal of an entropic functional s bg k sigma i p i ln p i for the bg formalism with the appropriate constraints sigma i p i 1 and sigma i p i e i u for the bg canonical ensemble second through optimization the equilibrium or stationary state distribution p i e betae i z bg with z bg sigma j e betae j for bg third the connection to thermodynamics e g f bg 1 beta ln z bg and u bg partial differential partial differential beta ln z bg assuming temperature fluctuations beck and cohen recently proposed a generalized boltzmann factor b e integral infinity 0 dbetaf beta e betae this corresponds to the second stage described above in this paper we solve the corresponding first stage i e we present an entropic functional and its associated constraints which lead precisely to b e we illustrate with all six admissible examples given by beck and cohen

dynamical pair approximation for cellular automata with shuffle update the random shuffle update method for the asymmetric exclusion process asep is introduced and the dynamical pair technique is extended in order to analyse its dynamics a sequence of approximate models is introduced the first element of which corresponds to the classical parallel update rule whose pair dynamics is reviewed it is then shown how the argument may be extended inductively to solve for the two cell configuration probabilities for each element of the sequence of approximate models a formal limit is then taken and macroscopic velocities and flow rates are derived

penalty techniques for state constrained optimal control problems with the wave equation we consider a system that is governed by a pde of hyperbolic type namely the wave equation and is controlled by a dirichlet boundary control for the penalization of terminal constraints we compare the convergence of three penalization techniques a differentiable penalty method an exact penalization and a smoothed exact penalization the error of the solution of the differentiably penalized problem is at most of the order 1 sqrt gamma where gamma is the penalty parameter the exact penalization yields the exact solution if gamma is sufficiently large if gamma is sufficiently large for the smoothed exact penalization we obtain an error bound of the order 1 sqrt beta where beta is the additional smoothing parameter this method yields differentiable objective functions that remain uniformly strongly convex since gamma need not tend to infinity to obtain convergence we also consider the penalization of distributed inequality state constraints that prescribe an upper bound for the l infty norm of the state we prove the convergence with respect to the l 2 norm for a penalization of the constraint violation measured in the l 1 norm we use this penalization technique to prove the existence of optimal controls for the inequality state constrained problem

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

generalized entropies from first principles a derivation of power law canonical distributions from first principle statistical mechanics including the exponential distribution as a particular case is presented it is shown that these distributions arise naturally and that the heat capacity of the heat bath is the condition that determines its type as a consequence a physical interpretation for the parameter q of the generalized entropy is given

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

thermodynamic equilibrium and its stability for microcanonical systems described by the sharma taneja mittal entropy it is generally assumed that the thermodynamic stability of equilibrium states is reflected by the concavity of entropy we inquire in the microcanonical picture about the validity of this statement for systems described by the two parametric entropy s kappa r of sharma taneja and mittal we analyze the composability rule for two statistically independent systems a and b described by the entropy s kappa r with the same set of the deformation parameters it is shown that in spite of the concavity of the entropy the composability rule modifies the thermodynamic stability conditions of the equilibrium state depending on the values assumed by the deformation parameters when the relation s kappa r a union b s kappa r a s kappa r b holds superadditive systems the concavity condition does imply thermodynamics stability otherwise when the relation s kappa r a union b s kappa r a s kappa r b holds subadditive systems the concavity condition does not imply thermodynamical stability of the equilibrium state

local structure theory for cellular automata abstract the mean field theory for cellular automata wolfram and schulman and seiden is generalized to the local structure theory the local structure theory is a sequence of finitely parameterized models of the statistical features of a cellular automaton s evolution the n th model in the sequence takes into account correlations in terms of the probability of blocks of n states a class of measures the n block measures is introduced the local structure operator of order n maps n block measures to n block measures in a manner which reflects the cellular automaton map on blocks of states the fixed points of the map on measures approximate the invariant measures of the cellular automaton the ability of the local structure theory to model evolution from uncorrelated initial distributions is studied the theory gives exact results in simple cases in more complex cases monte carlo numerical experiments suggest that an accurate statistical portrait of cellular automaton evolution is obtained the invariant measures of a cellular automaton and the stability of these measures may be obtained from the local structure theory the local structure theory appears to be a powerful method for characterization and classification of cellular automata nearest neighbor cellular automata with two states per cell are studied using this method

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

quantum vibrational partition function in the non extensive tsallis framework abstract the quantum vibrational partition function has been obtained in the tsallis statistics framework for the entropic index q between 1 and 2 the effect of non extensivity on the population of states and thermodynamic properties have been studied and compared with their corresponding values obtained in the boltzmann gibbs bg statistics our results show that the non extensive partition function of harmonic oscillator at any temperature is larger than its corresponding values for an extensive system and that their differences increase with temperature and entropic index also the number of accessible states increases with q but compared to the bg statistics the occupation number decreases for low energy levels while the population of the higher energy levels increases the internal energy and heat capacity have also been obtained for the non extensive harmonic oscillator system results indicate that the heat capacity is greater than its corresponding value in the extensive bg system at low temperatures but that this trend is reversed at higher temperatures

pdf of velocity fluctuation in turbulence by a statistics based on generalized entropy an analytical formula for the probability density function pdf of the velocity fluctuation in fully developed turbulence is derived non perturbatively by assuming that its underlying statistics is the one based on the generalized measures of entropy the renyi entropy or the tsallis entropy the parameters appearing in the pdf including the index q in the generalized measures are determined self consistently with the help of the observed value of the intermittency exponent the derived pdf explains quite well the experimentally observed density functions

the statistical distributions of one dimensional turbulence we study a one dimensional discrete analog of the von karman flow widely investigated in turbulence made of a lattice of anharmonic oscillators excited by both ends in the presence of a dissipative term proportional to the second order finite difference of the velocities similar to the viscous term in a fluid the dynamics of the model shows striking similarities with an actual turbulent flow both at local and global scales calculations of the probability distribution function of velocity increments extensively studied in turbulence with a very large number of points in order to determine accurately the statistics of rare events allow us to provide a meaningful comparison of different theoretical expressions of the pdfs

conditional lagrangian acceleration statistics in turbulent flows with gaussian distributed velocities the random intensity of noise approach to the one dimensional laval dubrulle nazarenko type model having deductive support from the three dimensional navier stokes equation is used to describe lagrangian acceleration statistics of a fluid particle in developed turbulent flows intensity of additive noise and cross correlation between multiplicative and additive noises entering a nonlinear langevin equation are assumed to depend on random velocity fluctuations in an exponential way we use an exact analytic result for the acceleration probability density function obtained as a stationary solution of the associated fokker planck equation we give a complete quantitative description of the available experimental data on conditional and unconditional acceleration statistics within the framework of a single model with a single set of fit parameters the acceleration distribution and variance conditioned on lagrangian velocity fluctuations and the marginal distribution calculated by using independent gaussian velocity statistics are found to be in a good agreement with the recent high reynolds number lagrangian experimental data the fitted conditional mean acceleration is very small that is in agreement with direct numerical simulations and increases for higher velocities but it departs from the experimental data which exhibit anisotropy of the studied flow

a note on the application of non extensive statistical mechanics to fully developed turbulence we show that the recent application of non extensive statistical mechanics to fully developed turbulence fdt satisfies novikov s inequality only in the near gaussian limit and exhibits compatibility with various other formulations of fdt we define relations between the non extensivity parameter q and the corresponding parameters of the lognormal multifractal and random model

dynamical systems of langevin type abstract dynamical systems of langevin type are deterministic mappings that arise if the gaussian white noise of a langevin equation is replaced by a deterministic chaotic dynamics we describe the various types of mappings that can be obtained in this way and investigate typical transition scenarios from complicated non gaussian to langevin like behavior that occur if a time scale parameter is changed we define a new characteristic quantify fir ergodic mappings called effective langevin radius which is related to the critical time scale where the marginal invariant density of the dynamical system of langevin type loses its differentiability the invariant density is shown to contain useful information on the entire characteristic functional of the chaotic driving force some general symmetry properties of the invariant densities are discussed

green kubo formula derived from large deviation statistics abstract numerical calculations for many physical systems including chaos and turbulence have been greatly developed in recent years we often investigate the characteristics of the time series for chaotic systems and study the essential laws underlying its time series we show the important characteristics which are sometimes not pointed out one of them is the green kubo formula which holds for the time series that satisfies the large deviation statistics extended version for the relation is shown in this paper and a simple example is given the relationship between the green kubo formula and the large deviation statistics is emphasized

quantum evolution of power law mixed states we study mixed quantum states described by a statistical operator bn n real with b quadratic in the position and momentum operators these states are parameterized as density matrices exhibiting the maximum q entropy q maxent form they can be regarded as the mixed state counterpart of the power law tail wave packets recently introduced by lillio and mantegna phys rev lett 84 2000 1061 84 2000 4516 we study the time evolution of these q maxent density matrices we also investigate the main features of their associated position probability distributions in particular we focus attention on the convergence of the concomitant moments

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators