nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

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

a nonextensive statistical approach to the kinetics of phase transformation abstract some limitations of johnson mehl avrami kolmogorov jmak equation which is used widely for describing kinetics of phase transformation were demonstrated using probabilistic analysis and monte carlo simulations acta mater 48 2000 4217 as well known jmak equation predicts correctly the real transformed fraction only if the number of the growing nuclei in the controlled volume is large however jmak equation seems to fail if the number of growing nuclei is small no matter how large the volume of the controlled volume is in this study we propose a different equation for describing kinetics of phase transformation using a nonextensive formalism namely tsallis thermostatistics which has been commonly employed to study the various physical systems for a decade

galilean invariant lattice boltzmann models with h theorem we demonstrate that the requirement of galilean invariance determines the choice of h function for a wide class of entropic lattice boltzmann models for the incompressible navier stokes equations the required h function has the form of the burg entropy for d 2 and of a tsallis entropy with q 1 2 d for d 2 where d is the number of spatial dimensions we use this observation to construct a fully explicit unconditionally stable galilean invariant lattice boltzmann model for the incompressible navier stokes equations for which attainable reynolds number is limited only by grid resolution

form invariance of differential equations in general relativity einstein equations for several matter sources in robertson walker and bianchi i type metrics are shown to reduce to a kind of second order nonlinear ordinary differential equation y f y f y f y dy f y 0 also it appears in the generalized statistical mechanics for the most interesting value q 1 the invariant form of this equation is imposed and the corresponding nonlocal transformation is obtained the linearization of that equation for any and is presented and for the important case f byn k with 2 n 1 n 2 2 its explicit general solution is found moreover the form invariance is applied to yield exact solutions of some other differential equations

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

free vibration analysis for tube in tube tall buildings an approximate solution procedure is formulated for free vibration analysis of tube in tube tall buildings in this paper the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients on the assumption that the transverse displacement is a harmonic vibration a power series solution which represents the mode shape function of tube in tube tall buildings is derived applying the boundary conditions yields the boundary value problem from which the frequency equation is established and solved through a numerical process to determine the natural frequencies two numerical examples are performed and compared with results available in the published literature to show the accuracy of the proposed method care has been exercised to retain sufficient terms in power series in evaluating natural frequencies of accepted accuracy the influences of the factors including flexural rigidity mass per unit length and building height to the natural frequency are discussed the method proposed herein enables one to calculate as an alternative the natural frequency of tube in tube tall buildings with good accuracy associated by calculators and hand prior to use of the complicated computer programs

sturm liouville equation for free vibration of a tube in tube tall building the equation for free vibration of a tube in tube tall building which is obtained by considering an influence coefficient due to the shear lag effect and using the equivalent closed tube method is proved strictly to be the fourth order sturm liouville differential equation and a formulation for calculating natural frequencies of the structure is obtained directly in comparison with other numerical and experimental results the frequencies found from the proposed method are quite satisfactory for practical use and are simple to calculate

nonextensivity of the cyclic lattice lotka volterra model this niteness only oc curs for q 0 5 for the d 2 growth mode growing droplet and for q 0 for the d 1 one growing stripe this strongevidence of nonextensivity is consistent with the spontaneousemergence of local domains of identical particles with fractalboundaries and competing interactions such direct evidenceis for the rst time exhibited for a many body system which at the mean eld level is conservative keywords lattice lotka volterra model fractals reac tion limited processes nonextensivity pacs numbers 5 40 a 05 10 ln 05 65 b 82 40 npmany natural and arti cial systems are known today tobe hardly or not at all tractable within boltzmann gibbsstatistical mechanics hence the usual thermodynamics suchis the case of systems which include long range interactionsor long range microscopic or mesoscopic memory or othersources of multi fractality phenomena where many spa tial and or temporal scales are involved typically exhibitpower laws the celebrated boltzmann gibbs bg entropys

measuring nonextensitivity parameters in a turbulent couette taylor flow we investigate probability density functions of velocity differences at different distances r measured in a couette taylor flow for a range of reynolds numbers re there is good agreement with the predictions of a theoretical model based on nonextensive statistical mechanics where the entropies are nonadditive for independent subsystems we extract the scale dependent nonextensitivity parameter q r mathrm re from the laboratory data

analytical solutions for the thick walled cylinder problem modeled with an isotropic elastic second gradient constitutive equation numerical modeling of localization phenomena shows that constitutive equations with internal length scale are necessary to properly model the post localization behavior moreover these models allow an accurate description of the scale effects observed in some phenomena like micro indentation this paper proposes some analytical results concerning a boundary value problem in a medium with microstructure in addition to their own usefulness such analytical solutions can be used in benchmark exercises for the validation of numerical codes the paper focuses on the thick walled cylinder problem using a general small strain isotropic elastic second gradient model the most general isotropic elastic model involving seven different constants is used and the expression of the analytical solutions is explicitly given the influence of the microstructure is controlled by the internal length scale parameter the classical macrostress is no more in equilibrium with the classical forces at the boundary double stresses are indeed also generated by the classical boundary conditions and as far as the microstructure effects become predominant i e the internal length scale is much larger than the thickness of the cylinder the macrostresses become negligible this leads to solutions completely different from classical elastic ones

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

universal renormalization group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics we uncover the dynamics at the chaos threshold m of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period doubling cascade that occurs for m m we corroborate this structure analytically via the feigenbaum renormalization group rg transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential of which we determine the q index and the q generalized lyapunov coefficientl q our results are an unequivocal validation of the applicability of the nonextensive generalization of boltzmann gibbs statistical mechanics to critical points of nonlinear maps critical points of nonlinear maps offer a suitable playground for testing the validity of the nonextensive generalization of the boltzmann gibbs bg statistical mechanics proposed by tsallis over a decade ago 1 2 here we describe universal properties related to the dynamics of iterates at the onset of chaos in unimodal maps 3 which provide a literal confirmation of the generalized nonextensive theory to this end we employ the celebrated one dimensional logistic map f m x 512muxu 2 21 x 1 and the properties of its renormalization group rg fixed point to present evidence of previously unexposed scaling properties at the onset of chaos m5m at this state the most prominent of the map critical points the trajectories of the iterates exhibit an intricate structure that we describe and show is governed by the feigenbaum rg transformation 3 the domain of validity of bg statistical mechanics has been implicitly challenged by the proposal of its nonextensive generalization subsequent studies have offered experimental and numerical evidence that point out both the inadequacy of the standard bg statistics and the plausible competence of the generalized theory in describing various types of phenomena and systems this theoretical development represents an exceptional event in the long and trustworthy history of bg statistical mechanics however it is still in the process of being converted into a rigorously corroborated and fully understood fact the suggested circumstances under which the generalized theory is believed to be applicable at least with regards to nonlinear dynamical systems are those associated to a phase space with power law sensitivity to initial conditions to the consequent vanishing of the largest lyapunov exponent and to a fractal or multifractal geometrical structure 2 here we show that our results for the dynamics at the onset of chaos in unimodal maps constitute an unequivocal proof of the universal validity of the nonextensive statistics at such critical points in fact at the chaos threshold as well as at other critical points of the map the lyapunov exponent l 1 vanishes and the sensitivity to initial conditions j t for large iteration time t ceases to obey exponential behavior exhibiting instead a power law behavior 4 in order to describe the dynamics at such critical points the q exponential expression

classical jacobi polynomials closed form solutions for transverse vibrations this paper deals with transverse vibrations of nonuniform homogeneous beams and plates classes of beams and axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations respectively can be reduced to an eigenvalue singular problem singularities occur at both ends of orthogonal polynomials are reported exact natural frequencies and jacobi polynomials as exact mode shapes which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials are reported for these classes the above classes of beams and plates hereafter called jacobi classes are given by geometry and boundary conditions the geometry consists of parabolic thickness variation with respect to the axial coordinate for beams and with respect to the radius for plates beams belonging to this class have either one or two sharp ends singularities along with certain boundary conditions plates have zero thickness at zero and outer radii the boundary value problems associated with plates and beams of two sharp ends are free boundary problems two other boundary value problems hinged free and sliding free are reported for beams with one sharp end also exact natural frequencies and mode shapes for uniformly rotating beams with hinged free boundary are reported

a nonextensive maximum entropy approach to a family of nonlinear reaction diffusion equations we consider a monoparametric family of reaction diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time dependent particular solutions of the tsallis maximum entropy maxent form the evolution of these solutions is governed by a system of three coupled nonlinear ordinary differential equations that are integrated numerically a simple population dynamics interpretation provides a qualitative understanding of the behaviour of the q maxent solutions when the reaction term vanishes the time dependent distributions studied here reduce to the previously known tsallis maxent solutions for the nonlinear diffusion equation

the effects of the nonextensivity on the dimerization process and nematic ordering abstract the influence of the dimerization process on the nematic ordering is investigated by using a nonextensive thermostatistics namely tsallis thermostatistics tt a theoretical model taking into account the dimerization influence on the nematic scalar order parameter has been recently presented phys lett a 256 1999 309 our study considers this model and the theoretical predictions for the nematic order parameter are improved by using tt

itineration of the internet over nonequilibrium stationary states in tsallis statistics the cumulative probability distribution of sparseness time interval in the internet is studied by the method of data analysis round trip time between a local host and a destination host through ten odd routers is measured using the ping command i e doing an echo experiment the data are found to be well described by q exponential distributions which maximize the tsallis entropy indexed by q less or larger than unity showing a scale invariant feature of the system the network is observed to itinerate over a series of the nonequilibrium stationary states characterized by tsallis statistics

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

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

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