why tsallis statistics abstract it is a remarkable fact that the traditional teaching of thermodynamics as reflected in the textbooks and including the long developments about ensembles and thermodynamic functions is almost entirely about systems in equilibrium the time variable does not enter there is one exception however the single most important item the flagship of the thermodynamic navy the second law is about the irreversibility of the time evolution of systems out of equilibrium this is a bizarre situation to say the least a glaring case of the drunk man looking for his key under the lamp post when he knows that he lost it in the dark part of the street the moment has come for us to go looking in the dark part the behavior of systems as a function of time we have been given a powerful new flashlight chaos theory we should use it there on the formerly dark pavement we can find tsallis statistics

replica ornstein zernike self consistent theory for mixtures in random pores we present a self consistent integral equation theory for a binary liquid in equilibrium with a disordered medium based on the formalism of the replica ornstein zernike roz equations specifically we derive direct formulas for the chemical potentials and the zero separation theorems the latter provide a connection between the chemical potentials and the fluid cavity distribution functions next we solve a modified verlet closure to roz equations which has built in parameters that can be adjusted to satisfy the zero separation theorems the degree of thermodynamic consistency of the theory is also kept under control we model the binary fluid in random pores as a symmetrical binary mixture of nonadditive hard spheres in a disordered hard sphere matrix and consider two different values of the nonadditivity parameter and of the quenched matrix packing fraction at different mixture concentrations we compare the theoretical structural properties as obtained through the present approach with percus yevick and martinov sarkisov integral equation theories and assess both structural and thermodynamic properties by performing canonical standard and biased grand canonical monte carlo simulations our theory appears superior to the other integral equation schemes here examined and provides reliable estimates of the chemical potentials this feature should be useful in studying the fluid phase behavior of model adsorbates in random pores in general

a theorem on the equilibrium thermodynamics of hamiltonian systems we prove a theorem stating that within an interesting class of stationary solutions of the liouville equation the tsallis q distributions are the only ones that satisfy a condition which guarantees the existence of an integrating factor for the heat the functional forms of the distribution as well as that of entropy temperature and heat capacity are derived we then explain why the gibbs distribution as a limit of the tsallis one plays a privileged role for large size ordinary molecular systems

new beams of global bifurcation points for a reaction diffusion system with inequalities or inclusions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that an obstacle e g a unilateral membrane modeled either in terms of inequalities or of inclusions introduces whole beams of new global bifurcation points of spatially non homogeneous stationary solutions which lie in parameter domains which are excluded as bifurcation points for the problem without the obstacle

dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

superstatistical generalization of the work fluctuation theorem abstract we derive a generalized version of the work fluctuation theorem for non equilibrium systems with spatio temporal temperature fluctuations for 2 distributed inverse temperature we obtain a generalized fluctuation theorem based on q exponentials whereas for other temperature distributions more complicated formulae arise since q exponentials have a power law decay the decay rate in this generalized fluctuation theorem is much slower than the conventional exponential decay this implies that work fluctuations can be of relevance for the design of micro or nano structures since the work done on the system is relatively much larger than in the conventional fluctuation theorem

galilean invariant multi speed entropic lattice boltzmann models abstract in recent work phys rev e 68 2003 025103 it was shown that the requirement of galilean invariance determined the form of the h function used in entropic lattice boltzmann models for the incompressible navier stokes equations in d dimensions the form obtained was that of the burg entropy for d 2 and the tsallis entropy with q 1 2 d for d 2 the conclusions obtained in that work were restricted to particles of a single mass and speed on a bravais lattice in this work we generalize the construction of such galilean invariant entropic lattice boltzmann models by allowing for certain models with multiple masses and speeds we show that the required h function for these models must be determined by solving a certain functional differential equation remarkably the solutions to this equation also have the form of the tsallis entropy where q is determined by the solution to a certain transcendental equation involving the dimension and symmetry properties of the lattice as well as the masses and speeds of the particles

bifurcation for a reaction diffusion system with unilateral and neumann boundary conditions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability if supplemented by pure neumann boundary conditions we show by a degree theoretic approach that an obstacle e g a unilateral membrane modeled in terms of inequalities introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable moreover this parameter domain is rather different from the known case when also dirichlet conditions are assumed in particular bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know

continuity compactness and degree theory for operators in systems involving p laplacians and inclusions the study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in sobolev spaces we show that under natural assumptions this operator has the properties which allow to apply degree theory fixed point index for multivalued maps more precisely this operator is upper semicontinuous and compact with nonempty convex compact values for the particular case of systems involving p laplacians we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available

bifurcation points for a reaction diffusion system with two inequalities abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that obstacles e g a unilateral membrane for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles

the abc of hyper recursions each member of the family of gauss hypergeometric functions fn 2f1 a e1n b e2n c e3n z where a b c and z do not depend on n and ej 0 1 not all ej equal to zero satisfies a second order linear difference equation of the form anfn 1 bnfn cnfn 1 0 because of symmetry relations and functional relations for the gauss functions the set of 26 cases for different ej values can be reduced to a set of 5 basic forms of difference equations in this paper the coefficients an bn and cn of these basic forms are given in addition domains in the complex z plane are given where a pair of minimal and dominant solutions of the difference equation have to be identified the determination of such a pair asks for a detailed study of the asymptotic properties of the gauss functions fn for large values of n and of other gauss functions outside this group this will be done in a later paper

quantum statistical mechanics for nonextensive systems the traditional basis of description of many particle systems in terms of green functions is here generalized to the case when the system is nonextensive by incorporating the tsallis form of the density matrix indexed by a nonextensive parameter q this is accomplished by expressing the many particle q green function in terms of a parametric contour integral over a kernel multiplied by the usual grand canonical green function which now depends on this parameter we study one and two particle green functions in detail from the one particle green function we deduce some experimentally observable quantities such as the one particle momentum distribution function and the one particle energy distribution function special forms of the two particle green functions are related to physical dynamical structure factors some of which are studied here we deduce different forms of sum rules in the q formalism a diagrammatic representation of the q green functions similar to the traditional ones follows because the equations of motion for both of these are formally similar approximation schemes for one particle q green functions such as hartree and hartree fock schemes are given as examples this extension enables us to predict possible experimental tests for the validity of this framework by expressing some observable quantities in terms of the q averages

nonextensive foundation of levy distributions a deep connection between the ubiquity of l evy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently tsallis et al phys rev lett 75 3589 1995 by using unnormalized q expectation values it has just been argued on physical grounds that normalized q expectation values should be used instead we revisit within this more appropriate scheme the l evy problem and verify that the relevant analytic results become sensibly simplified whereas the basic physics remains unchanged

stock market return distributions from past to present abstract we show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short minute time scales exhibit power scaling with the scaling index 3 and this index tends to increase quickly with decreasing sampling frequency our study is based on high frequency recordings of the s p500 dax and wig20 indices over the interval may 2004 may 2006 our findings suggest that dynamics of the contemporary market may differ from the one observed in the past this effect indicates a constantly increasing efficiency of world markets

density functional theory for fluids in porous media as models for substances adsorbed within amorphous solid matrices we consider mixtures of spheres with either hard or ideal interactions where several matrix components are quenched and the remaining adsorbate components are equilibrated we propose a density functional theory based on the exact zero dimensional limit which treats both matrix and adsorbate components on the level of the respective one body density profiles as a test we calculate pair correlation functions for hard spheres adsorbed in either a hard sphere or an ideal sphere matrix and find good agreement with our computer simulation results

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

computing a non maxwellian velocity distribution from first principles we investigate a family of single particle anomalous velocity distribution by solving a particular class of stochastic liouville equations the stationary state is obtained analytically and the maxwell boltzmann distribution is reobtained in a particular limit we discuss the comparison with other different methods to obtain the stationary state extensions when the models cannot be solved in an exact way are also pointed out in connection with the one ficton approximation

relaxation in heterogeneous systems a rare events dominated phenomenon abstract we have derived a general two power law relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems the power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q for intermediate times the relaxation follows a stretched exponential behavior the asymptotic power law behaviors both in the time and the frequency domains coincide with those of the weron generalized dielectric function derived in the stochastic theory from an extension of the levy central limit theorem these results are in full agreement with the jonscher universality principle and trace the origin of the large t power law universality with system dependent exponent and q to the scaling behavior of the extreme value distribution function of the effective macroscopic waiting time and the fluctuation of the number of relaxing entities

random sequential adsorption of polydisperse spherical particles an integral equation theory abstract our previously developed integral equation theories were applied to incorporate the effect of polydispersity in the study of the random sequential addition of spherical particles by using the simplest uniform size distribution we found that results from theories were in consistence with the monte carlo simulation results some deviations were seen which resulted from the exclusion effects of polydisperse particles it was found in the simulations that with increasing densities small particles adsorbed preferentially and the size distribution skewed towards the smaller particles therefore to accurately predict the correct radial distribution functions the more appropriate size distributions are needed for all size ranges which were 0 40 d 1 60 d 0 75 d 1 25 d and 0 90 d 1 10 d the radial distribution functions from theory at number densities of 0 2 0 4 and 0 65 were in good agreements with those from the simulations

modelling train delays with q exponential functions we demonstrate that the distribution of train delays on the british railway network is accurately described by q exponential functions we explain this by constructing an underlying superstatistical model

on the contiguous relations of hypergeometric series contiguous relations are a fundamental concept within the theory of hypergeometric series and orthogonal polynomials their study goes back to gauss who gave a list of 15 fundamental relations for the 2f1 hypergeometric series in this paper we will prove some consequences of contiguous relations of 2f1

metastable states anomalous distributions and correlations in the hmf model abstract we study the microscopic dynamics of the metastable quasi stationary states qss in the hamiltonian mean field hmf model a hamiltonian system of n classical inertial spins with infinite range interactions which shows a second order phase transition in order to understand the origin of metastability which appears in an energy region below the critical point we consider two different classes of out of equilibrium initial conditions both leading to qss and having respectively initial magnetization equal to one m1 ic and equal to zero m0 ic we compare the corresponding space the resulting velocity pdfs and correlations and the eventual aging features of the microscopic dynamics in both cases the model exhibits nongaussian pdfs though anomalous correlations are present only when the system is started with an initial magnetization equal to one in the m0 ic case the relaxation to equilibrium is almost exponential while for m1 ic when correlations and aging are found the decay is a power law and the overall behavior can be very well reproduced by a tsallis q exponential function these results contribute to clarify the overall scenario which is more complex than previously expected and stress the importance of the dynamics in the relaxation process the nonextensive statistical mechanics formalism proposed by tsallis seems to be valid in the out of equilibrium phase when correlations and strong long term memory effects emerge this regime becomes stable if the n limit is performed before the t limit

density profiles of hard spheres in a cylinder filled with disordered matrix application of the born green yvon equation abstract local densities of a hard sphere fluid in a cylindrical pore filled with quenched disordered hard sphere matrix are calculated using born green yvon equation with fisher methfessel approximation the solution of replica ornstein zernike equation in the percus yevick approximation for a fluid in a homogeneous matrix is used as an input a comparison of the density profiles with simulation data shows that the theory works satisfactorily for the considered matrix and fluid densities

tsallis entropy production for diffusion on the diluted hypercube abstract we investigate the production of tsallis entropy for the probability distribution of random walkers on a hypercube with a fraction p of allowed sites we consider two regimes p 1 and from p 1 2 until the percolation limit pc in the first regime we show that the entropy rate can be obtained from the boltzmann gibbs shannon entropy time evolution on the second regime the same numerical experiments indicate a trivial limit for this quantity while by measuring the production of tsallis entropy for different q values there exists a particular value for the entropic index q that adequately describe the relaxation these results are compared to similar numerical experiments performed with non linear maps and indicate an analogy between the phase space of both systems

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

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

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

nonextensive statistical features of the polish stock market fluctuations the statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics here we present a systematic study of such characteristics for the polish stock market index wig20 over the period 04 01 1999 31 10 2005 for the time lags ranging from 1min1min up to 1 h this market is commonly classified as emerging still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power law as identified previously for majority of the mature markets within the time scales studied a quick and considerable departure from this law towards a gaussian can however be traced interestingly all the forms of the distributions observed can be comprised by the single q gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation the corresponding nonextensivity parameter q was found to systematically decrease when increasing the time scales the temporal correlations quantified here in terms of multifractality provide further arguments in favor of nonextensivity

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

bifurcation points and eigenvalues of inequalities of reaction diffusion type on demontre certaines assertions concernant les points de bifurcation et les valeurs propres de systemes de reaction diffusion avec des conditions unilaterales

the replica ornstein zernike equations and the structure of partly quenched media abstract we derive the replica ornstein zernike equations roz satisfied by the two point correlation functions for a partly quenched system i e a system in which some of the particles are quenched or frozen in place and some are annealed or allowed to equilibrate a formally exact closure for these equations is given a set of integral equations given by madden and glandt are recovered as an approximation to the exact roz equations we discuss the fundamental status of this approximation we also present new exact relations that express the thermodynamic quantities of partly quenched media using the canonical ensemble in terms of the correlation functions in such media

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

a method for selecting the bin size of a time histogram the time histogram method is the most basic tool for capturing a time dependent rate of neuronal spikes generally in the neurophysiological literature the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by individual researchers here we propose a method for objectively selecting the bin size from the spike count statistics alone so that the resulting bar or line graph time histogram best represents the unknown underlying spike rate for a small number of spike sequences generated from a modestly fluctuating rate the optimal bin size may diverge indicating that any time histogram is likely to capture a spurious rate given a paucity of data the method presented here can nevertheless suggest how many experimental trials should be added in order to obtain a meaningful time dependent histogram with the required accuracy

the analytic continuation of the gaussian hypergeometric function 2 f 1 a b c z for arbitrary parameters abstract our objective is to provide a complete table of analytic condinuation formulas for the gaussian hypergeometric function 2f1 a b c z which allow its fast and accurate computation for arbitrary values of z and of the parameters a b c to this end we distinguish 12 basis sets of the two dimensional space of the solutions of the hypergeometric differential equation representing 2f1 in each of them yields 12 analytic continuation formulas each two of them are series in one of the arguments z z z 1 1 z 1 1 z 1 z 1 1 z respectively such that any given argument z with the exception of two single points in the complex plane lies in the convergence domain of at least one of them we present rapidly converging series representations of 2f1 for all possible constellations of parameters for minimizing the effort for the derivation of these series we have extensively used the symmetry group of the hypergeometric equation which is shown to be isomorphic to the cubic group oh

degree instability and bifurcation of reaction diffusion systems with obstacles near certain hyperbolas abstract for a reaction diffusion system which is subject to turing s diffusion driven instability and which is equipped with unilateral obstacles of various types the nonexistence of bifurcation of stationary solutions near certain critical parameter values is proved the result implies assertions about a related mapping degree which in turn implies for small obstacles the existence of a new branch of bifurcation points spatial patterns induced by the obstacle

heavy tailed value at risk analysis for malaysian stock exchange abstract this article investigates the comparison of power law value at risk var evaluation with quantile and non linear time varying volatility approaches a simple pareto distribution is proposed to account the heavy tailed property in the empirical distribution of returns alternative var measurement such as non parametric quantile estimate is implemented using interpolation method in addition we also used the well known two components arch modelling technique under the assumptions of normality and heavy tailed student t distribution for the innovations our results evidenced that the predicted var under the pareto distribution exhibited similar results with the symmetric heavy tailed long memory arch model however it is found that only the pareto distribution is able to provide a convenient framework for asymmetric properties in both the lower and upper tails

semi nonparametric var forecasts for hedge funds during the recent crisis abstract the need to provide accurate value at risk var forecasting measures has triggered an important literature in econophysics although these accurate var models and methodologies are particularly demanded for hedge fund managers there exist few articles specifically devoted to implement new techniques in hedge fund returns var forecasting this article advances in these issues by comparing the performance of risk measures based on parametric distributions the normal student s t and skewed t semi nonparametric snp methodologies based on gram charlier gc series and the extreme value theory evt approach our results show that normal student s t and skewed t based methodologies fail to forecast hedge fund var whilst snp and evt approaches accurately success on it we extend these results to the multivariate framework by providing an explicit formula for the gc copula and its density that encompasses the gaussian copula and accounts for non linear dependences we show that the var obtained by the meta gc accurately captures portfolio risk and outperforms regulatory var estimates obtained through the meta gaussian and student s t distributions

distribution functions for fluids in random media a random medium is considered composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure statistically homogeneous on all but molecular length scales the equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed various particle particle and particle obstacle correlation functions which differ from the corresponding functions for a fully equilibrated binary mixture are defined through an averaging process over the static ensemble of obstacle configurations and application of topological reduction techniques the ornstein zernike equations also differ from their equilibrium counterparts

adsorption of dimerizing fluids in disordered porous networks abstract we consider the application of the integral equation theory to the study of associative fluids in disordered porous networks the theory also takes into account associative fluid network interactions the calculations reported here illustrate the effect of associative forces on the fluid fluid and fluid network correlation functions we find that an associative interaction gives rise to a strong intracore peak in the correlation functions but dampens the peaks outside the core

two dimensional maps at the edge of chaos numerical results for the henon map the mixing properties or sensitivity to initial conditions of the two dimensional henon map have been explored numerically at the edge of chaos three independent methods which have been developed and used so far for one dimensional maps have been used to accomplish this task these methods are i the measure of the divergence of initially nearby orbits ii analysis of the multifractal spectrum and iii computation of nonextensive entropy increase rates the results obtained closely agree with those of the one dimensional cases and constitute a verification of this scenario in two dimensional maps this obviously makes the idea of weak chaos even more robust

rates of convergence of non extensive statistical distributions to levy distributions in full and half spaces the levy type distributions are derived using the principle of maximum tsallis non extensive entropy both in the full and half spaces the rates of convergence to the exact levy stable distributions are determined by taking the n fold convolutions of these distributions the marked difference between the problems in the full and half spaces is elucidated analytically it is found that the rates of convergence depend on the ranges of the levy indices an important result emerging from the present analysis is deduced if interpreted in terms of random walks implying the dependence of the asymptotic long time behaviours of the walks on the ranges of the levy indices if n is identified with the total time of the walks

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

critique of q entropy for thermal statistics during the past 12 years there have been numerous papers on a relation between entropy and probability which is nonadditive and has a parameter q that depends on the nature of the thermodynamic system under consideration for q 1 this relation corresponds to the boltzmann gibbs entropy but for other values of q it is claimed that it leads to a formalism that is consistent with the laws of thermodynamics however it is shown here that the joint entropy for systems having different values of q is not defined in this formalism and consequently fundamental thermodynamic concepts such as temperature and heat exchange cannot be considered for such systems moreover for q ensuremath ne 1 the probability distribution for weakly interacting systems does not factor into the product of the probability distribution for the separate systems leading to spurious correlations and other unphysical consequences e g nonextensive energy that have been ignored in various applications given in the literature

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

on the closed form solutions for non extensive value at risk abstract we examine possible closed form solutions for the cumulative distribution function for systems where the probability density function can be adequately described by the generalized non extensive statistics framework application to financial time series as a possible value at risk technique indicates reasonable agreement with the data under consideration including all possible extremes and asymmetries of the returns numerical results to illustrate the efficiency of the method are presented

convergence to the critical attractor of dissipative maps log periodic oscillations fractality and nonextensivity for a family of logisticlike maps we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space we found that the phase space volume occupied by the ensemble w t depicts a power law decay with log periodic oscillations reflecting the multifractal character of the critical attractor we explore the parametric dependence of the power law exponent and the amplitude of the log periodic oscillations with the attractor s fractal dimension governed by the inflection of the map near its extremal point further we investigate the temporal evolution of w t for the circle map whose critical attractor is dense in this case we found w t to exhibit a rich pattern with a slow logarithmic decay of the lower bounds these results are discussed in the context of nonextensive tsallis entropies

derivation of nonlinear fokker planck equations by means of approximations to the master equation nonlinear fokker planck equations fpes are derived as approximations to the master equation in cases of transitions among both discrete and continuous sets of states the nonlinear effects introduced through the transition probabilities are argued to be relevant for many real phenomena within the class of anomalous diffusion problems the nonlinear fpes obtained appear to be more general than some previously proposed on a purely phenomenological basis ones in spite of this the same kind of solution applies i e it is shown that the time dependent tsallis s probability distribution is a solution of both equations obtained either from discrete or continuous sets of states and that the corresponding stationary solution is in the infinite time limit a stable solution

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

degree and global bifurcation for elliptic equations with multivalued unilateral conditions abstract a bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered the existence of global bifurcation between two eigenvalues of a certain type of the laplacian is proved for a class of abstract inclusions with compact multivalued mappings in a hilbert space it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single valued problem and the jump of the degree is proved as a consequence global bifurcation for such abstract inclusions is obtained the weak formulation of the boundary value problem mentioned is a particular case

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