classical and quantum conformational analysis using generalized genetic algorithm abstract recently the generalized genetic algorithm has been proposed based on genetic algorithms and tsallis statistics here we study molecular preferences of the simple molecules and polypeptides by coupling the generalized genetic algorithm and both a classical force field and a semi empirical quantum mechanics procedure the main characteristics of this stochastic algorithm is the capability to find the greatest number of minima for a given energy in an n dimensional hyper surface supplying information about the visiting rates for each one of the conformational structures the main advantage of this method over other global optimization procedures is that this approach provides additional information about visiting frequency of all local and global minima these characteristics may provide the populations of each conformation without using the quantum or classical monte carlo procedure

rigorous properties and uncertainty like relationships on product complexity measures application to atomic systems most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework valid for any arbitrary n dimensional distribution in the present work different product complexities constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated different results on product complexities such as rigorous bounds uncertainty like inequalities relationships among themselves and also statistical interpretations are given for the sake of completeness some of these analytical results on product complexities are numerically checked for the one particle densities of atomic systems in both conjugated spaces

renormalization in quantum field theory an improved rigorous method the perturbative construction of the s matrix in the causal spacetime approach of epstein and glaser may be interpreted as a method of regularization for divergent feynman diagrams the results of any method of regularization must be equivalent to those obtained from the epstein glaser eg construction within the freedom left by the latter in particular the conceptually well defined approach of bogoliubov parasiuk hepp and zimmermann bphz though conceptually different from eg meets this requirement based on this equivalence we propose a modified bphz procedure which provides a significant simplification of the techniques of perturbation theory and which applies equally well to standard quantum field theory and to chiral theories we illustrate the proposed method by a number of examples of various orders in perturbation theory at the level of multi loop diagrams we confirm that subdiagrams as classified by zimmermann s forest formula in bphz can be restricted to subdiagrams in the sense of epstein glaser thus entailing an important reduction of actual computations the relationship of our approach to the method of dimensional regularization and renormalization is particularly transparent without having to invoke analytic continuation to unphysical spacetime dimension it sheds new light on the role of some parameters that appear within the dimensional regularization and thus establishes a direct link of this traditional method to the bphz scheme

nonextensive triangle equality and other properties of tsallis relative entropy minimization kullback leibler relative entropy has unique properties in cases involving distributions resulting from relative entropy minimization tsallis relative entropy is a one parameter generalization of kullback leibier relative entropy in the nonextensive thermostatistics in this paper we present the properties of tsallis relative entropy minimization and present some differences with the classical case in the representation of such a minimum relative entropy distribution we highlight the use of the q product an operator that has been recently introduced to derive the mathematical structure behind the tsallis statistics one of our main results is the generalization of triangle equality of relative entropy minimization to the nonextensive case

gamma function to beck cohen superstatistics abstract in this paper we show a mathematical construction of beck cohen superstatistics in the bayesian point of view with the help of the two representations of a gamma function furthermore it is shown how some results for superstatistics are related to each other

stock market and motion of a variable mass spring we establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock market dynamics within an economic model based on simple temporal demand and supply functions e canessa j phys a 33 2000 3637 the total system energy et is shown to be proportional to a decreasing time dependent spring constant kt this model allows to derive log periodicity cos log t tc on commodity prices and oscillations surplus and shortages in the level of stocks we also made an attempt to connect these results to the tsallis statistics parameter q based on a possible force entropy correlation e canessa physica a 341 2004 165 and find that the tsallis second entropic term i 1wpiq q 1 relates to the square of the demand or supply function

quantum corrections for general partition functions abstract the classical limit for quite general partition functions is obtained using coherent states in this framework a general procedure is presented to obtain all the quantum corrections to the classical limit in particular the first and second order corrections are worked out explicitly and the classical limit for the tsallis thermostatistics is determined the results of this work generalize the ones obtained by wigner phys rev 40 1932 749 for usual statistical mechanics

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

age innovations and time operator of networks abstract we extend the time operator and age to network evolution models internal age formulas and the distribution of innovations are computed for erd s renyi random networks for markov networks and barabasi albert preferential attachment networks the innovation probabilities are found to be proportional to the quadratic entropy which coincides with the tsallis entropy for entropic index q 2 in all markov networks as well as in the linear growth mechanism the distribution of innovations in the barabasi albert model is a new probability distribution of the logarithmic type

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

large heterocline orbits for some evolution equations soit s r ou est un domaine borne de r n avec une frontiere reguliere on etudie l existence des orbites heteroclines pour u f u 0 dans s u 0 sur s avec f c 1 r r satisfaisant certaines conditions

a generalized statistical complexity measure applications to quantum systems a two parameter family of complexity measures c based on the renyi entropies is introduced and characterized by a detailed study of its mathematical properties this family is the generalization of a continuous version of the lopez ruiz mancini calbet complexity which is recovered for 1 and 2 these complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system when one of the parameters or goes to infinity one of the global factors becomes a local factor for this special case the complexity is calculated on different quantum systems h atom harmonic oscillator and square well

harmonious representation of pdfs reflecting large deviations abstract the framework of multifractal analysis mfa is distilled to the most sophisticated one within this transparent framework it is shown that the harmonious representation of mfa utilizing two distinct tsallis distribution functions one for the tail part of probability density function pdf and the other for its center part explains the recently observed pdfs of turbulence in the highest accuracy superior to the analyses based on other models such as the log normal model and the p model

entropic nonextensivity as a measure of time series complexity abstract information entropy is applied to the analysis of time series generated by dynamical systems complexity of a temporal or spatio temporal signal is defined as the difference between the sum of entropies of the local linear regions of the trajectory manifold and the entropy of the globally linearized manifold when the entropies are tsallis entropies the complexity is characterized by the value of q

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

steering in spin tomographic probability representation abstract the steering property known for two qubit state in terms of specific inequalities for the correlation function is translated for the state of qudit with the spin j 3 2 since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems the tomographic probability representation for the qudit states is applied the connection between the correlation function in the two qubit system and the single qudit is presented in an integral form with an intertwining kernel calculated explicitly in tomographic probability terms

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

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

a new class of entropic information measures formal group theory and information geometry in this work we study generalized entropies and information geometry in a group theoretical framework we explore the conditions that ensure the existence of some natural properties and at the same time of a group theoretical structure for a large class of entropies in addition a method for defining new entropies using previously known ones with some desired group theoretical properties is proposed in the second part of this work the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied finally a method of constructing new divergences from known ones is discussed in particular some results concerning the riemannian structure associated with the class of divergences under investigation are formulated

the renormalization group and optimization of non extensive entropy criticality in non linear one dimensional maps abstract we examine the pitchfork and tangent bifurcations in unimodal maps to illustrate a connection between renormalization group rg fixed points and entropy extremal properties we observe that the exact rg solution for the tangent bifurcation is also applicable to the period doubling cascade and assess its physical meaning since the expression for the fixed point map can be put into the form of the non extensive expressions for the temporal evolution of phase space volume and sensitivity of initial conditions we conclude that the map critical points possess the properties of this formalism the universality of the rg solution makes this interpretation inclusive to all one dimensional maps of non linearity z 1

dimensional regularization and renormalization of qed we give an space definition of dimensional regularization suited to the tree expansion method of renormalization we apply the dimensionally regularized tree expansion to qed obtaining sharp bounds on the size of a renormalized graph subtractions are made with the lagrangian counterterms of the tree expansion not by minimal subtraction techniques and so do not entail a knowledge of the meromorphic structure of a graph as a function of dimension this renormalization procedure respects the ward identities and the counterterms required are gauge invariant

diagram techniques for confluence abstract we develop diagram techniques for proving confluence in abstract reductions systems the underlying theory gives a systematic and uniform framework in which a number of known results widely scattered throughout the literature can be understood these results include newman s lemma lemma 3 1 of winkler and buchberger the hindley rosen lemma the request lemmas of staples the strong confluence lemma of huet the lemma of de bruijn

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

entropy and complexity analysis of dirac delta like quantum potentials abstract the dirac delta like quantum mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics condensed matter and quantum computation the entropy and complexity properties of potentials with one and two dirac delta functions are here analytically calculated and numerically discussed in both position and momentum spaces we have studied the information theoretic lengths of fisher renyi and shannon types as well as the cramer rao fisher shannon and lmc shape complexities of the lowest lying stationary states of one delta and twin delta they allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation

closer look at time averages of the logistic map at the edge of chaos the probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown see u tirnakli c beck and c tsallis phys rev e 75 040106 r 2007 to be numerically consistent with a q gaussian the distribution which under appropriate constraints maximizes the nonadditive entropy sq the basis of nonextensive statistical mechanics this analysis was based on a study of the tails of the distribution we now check the entire distribution in particular its central part this is important in view of a recent q generalization of the central limit theorem which states that for certain classes of strongly correlated random variables the rescaled sum approaches a q gaussian limit distribution we numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a q gaussian both in the central region and in the tail region and find a scaling law involving the feigenbaum constant our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy sq and its associated concepts

bi simulations up to characterise process semantics we define bi simulations up to a preorder and show how we can use them to provide a coinductive bi simulation like characterisation of semantic equivalences preorders for processes in particular we can apply our results to all the semantics in the linear time branching time spectrum that are defined by preorders coarser than the ready simulation preorder the relation between bisimulations up to and simulations up to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders in particular we have shown that the simulation up to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation since all of these canonical preorders are defined in an homogeneous way we can prove properties for them in a generic way as an illustrative example of this technique we generate an axiomatic characterisation of each of these canonical preorders that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time branching time spectrum whose correctness and completeness can be proved once and for all although we first prove by induction our results for finite processes then we see by using continuity arguments that they are also valid for infinite finitary processes

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

statistical analysis of geopotential height gh timeseries based on tsallis non extensive statistical mechanics abstract in this paper we perform statistical analysis of time series deriving from earth s climate the time series are concerned with geopotential height gh and correspond to temporal and spatial components of the global distribution of month average values during the period 1948 2012 the analysis is based on tsallis non extensive statistical mechanics and in particular on the estimation of tsallis q triplet namely q stat q sens q rel the reconstructed phase space and the estimation of correlation dimension and the hurst exponent of rescaled range analysis r s the deviation of tsallis q triplet from unity indicates non gaussian tsallis q gaussian non extensive character with heavy tails probability density functions pdfs multifractal behavior and long range dependences for all timeseries considered also noticeable differences of the q triplet estimation found in the timeseries at distinct local or temporal regions moreover in the reconstructive phase space revealed a lower dimensional fractal set in the gh dynamical phase space strong self organization and the estimation of hurst exponent indicated multifractality non gaussianity and persistence the analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth s climate

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

on the putative essential discreteness of q generalized entropies abstract it has been argued in abe 2010 entitled essential discreteness in generalized thermostatistics with non logarithmic entropy that continuous hamiltonian systems with long range interactions and the so called q gaussian momentum distributions are seen to be outside the scope of non extensive statistical mechanics the arguments are clever and appealing we show here that however some mathematical subtleties render them unconvincing

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

on the stability of generalized entropies by the use of a probabilistic coupling technique and generalizing a recent result of zhang 2007 lett math phys 80 171 we derive several sharp inequalities concerning the uniform continuity of some generalized entropies these inequalities capture certain aspects of the interplay between the entropies and the uniform distance variational distance and establish the stability of the involved entropies

dimensional regularization in position space and a forest formula for epstein glaser renormalization we reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time ordered products as solutions to the induction scheme of epstein glaser this closed expression which we call the epstein glaser forest formula is analogous to zimmermann s forest formula for bph renormalization for scalar fields the resulting renormalization method is always applicable we compute several examples we also analyze the hopf algebraic aspects of the combinatorics our starting point is the main theorem of renormalization of stora and popineau and the arising renormalization group as originally defined by stuckelberg and petermann

on a comparative study between dependence scales determined by linear and non linear measures in this manuscript we present a comparative study about the determination of the relaxation i e independence time scales obtained from the correlation function the mutual information and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy our results show that for systems with a small degree of complexity standard mutual information and the criterion based on its nonextensive generalisation provide the same scale whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller

indices for testing neural codes one of the most critical challenges in systems neuroscience is determining the neural code a principled framework for addressing this can be found in information theory with this approach one can determine whether a proposed code can account for the stimulus response relationship specifically one can compare the transmitted information between the stimulus and the hypothesized neural code with the transmitted information between the stimulus and the behavioral response if the former is smaller than the latter i e if the code cannot account for the behavior the code can be ruled out the information theoretic index most widely used in this context is shannon s mutual information the shannon test however is not ideal for this purpose while the codes it will rule out are truly nonviable there will be some nonviable codes that it will fail to rule out here we describe a wide range of alternative indices that can be used for ruling codes out the range includes a continuum from shannon information to measures of the performance of a bayesian decoder we analyze the relationship of these indices to each other and their complementary strengths and weaknesses for addressing this problem

extremum entrop y based heisenberg like uncertainty relations in this work we use the extremization method of various information theoretic measures fisher information shannon entropy tsallis entropy for d dimensional quantum systems which complementarily describe the spreading of the quantum states of natural systems under some given constraints usually one or two radial expectation values this variational method allows us to determine an extremum entropy distribution which is the least biased one to characterize the state among all those compatible with the known data then we use it together with the spin dependent uncertainty like relations of daubechies thakkar type as a tool to obtain relationships between the position and momentum radial expectation values of the type for d dimensional systems of n fermions with spin s the resulting uncertainty like products which take into account both spatial and spin degrees of freedom of the fermionic constituents of the system are shown to often improve the best corresponding relationships existing in the literature

tsallis based variational method for finding approximate wave functions abstract we introduce trial functions of a form that maximizes a tsallis information measure and use them in conjunction with the variational approach of cooper dawson and shepard cds that is based upon supersymmetry ideas

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

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

dimensionally regularized tsallis statistical mechanics and two body newton s gravitation abstract typical tsallis statistical mechanics quantifiers like the partition function and the mean energy exhibit poles we are speaking of the partition function z and the mean energy u the poles appear for distinctive values of tsallis characteristic real parameter q at a numerable set of rational numbers of the q line these poles are dealt with dimensional regularization resources the physical effects of these poles on the specific heats are studied here for the two body classical gravitation potential

diffusion on fractal phase spaces and entropy production abstract complex systems may show strongly non exponential relaxation the origins of these behavior seem to be related to the fractal structure of the phase space in this article we consider the diffusion on a dilute hypercube this stochastic process is a coarse grained model for the time evolution of a glassy system where both the dynamics and the structure of the phase space was considered as simple as possible we characterize this process using two quantities a memory function and the tsallis entropy the first one is a measure of mixing while the second is related to non extensivity we characterize quantitatively their relationship finally we discuss the implications for other glassy and complex systems

new up to techniques for weak bisimulation up to techniques have been introduced to enhance the bisimulation proof method for establishing bisimilarity results while up to techniques for strong bisimilarity are well understood the irregularities that appear in the weak case make it difficult to give a unified presentation we propose a uniform and modular theory of up to techniques for weak bisimulation that captures most of the existing proof technology and introduces new techniques some proofs rely on nontrivial and new commutation results based on termination guarantees all results presented in this paper have been formally proved using the coq proof assistant

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

troublesome aspects of the renyi maxent treatment we study in great detail the possible existence of a renyi associated thermodynamics with negative results in particular we uncover a hidden relation in renyi s variational problem maxent this relation connects the two associated lagrange multipliers canonical ensemble with the mean energy u and the renyi parameter as a consequence of such relation we obtain anomalous renyi maxent thermodynamic results

solution of fractional kinetic equation by a class of integral transform of pathway type solutions of fractional kinetic equations are obtained through an integral transform named p transform introduced in this paper the p transform is a binomial type transform containing many class of transforms including the well known laplace transform the paper is motivated by the idea of pathway model introduced by mathai linear algebra appl 396 317 328 2005 10 1016 j laa 2004 09 022 the composition of the transform with differential and integral operators are proved along with convolution theorem as an illustration of applications to the general theory of differential equations a simple differential equation is solved by the new transform being a new transform the p transform of some elementary functions as well as some generalized special functions such as h function g function wright generalized hypergeometric function generalized hypergeometric function and mittag leffler function are also obtained the results for the classical laplace transform is retrieved by letting 1

zeroth law compatibility of nonadditive thermodynamics nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules corrected in this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics we find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these our result offers a possible solution to the long standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

q exponential weibull and q weibull distributions an empirical analysis abstract in a comparative study the q exponential and weibull distributions are employed to investigate frequency distributions of basketball baskets cyclone victims brand name drugs by retail sales and highway length in order to analyze the intermediate cases a distribution the q weibull one which interpolates the q exponential and weibull ones is introduced it is verified that the basketball baskets distribution is well described by a q exponential whereas the cyclone victims and brand name drugs by retail sales ones are better adjusted by a weibull distribution on the other hand for highway length the q exponential and weibull distributions do not give satisfactory adjustment being necessary to employ the q weibull distribution furthermore the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law q exponential with q 1 controversy

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

irreversibility entropy and incomplete information abstract the open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a p a measure but the p a measure is not yet known consequently it is difficult to develop the statistical thermodynamics for an irreversible system here its integral expression is obtained in order to its use in the statistical thermodynamic analysis of the complex and irreversible systems

third law of thermodynamics as a key test of generalized entropies the laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level the third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium conversely the entropy can vanish only at absolute zero temperature here we ask whether or not generalized entropies satisfy this fundamental property we propose a direct analytical procedure to test if a generalized entropy satisfies the third law assuming only very general assumptions for the entropy s and energy u of an arbitrary n level classical system mathematically the method relies on exact calculation of ds du in terms of the microstate probabilities pi to illustrate this approach we present exact results for the two best known generalizations of statistical mechanics specifically we study the kaniadakis entropy s which is additive and the tsallis entropy sq which is nonadditive we show that the kaniadakis entropy correctly satisfies the third law only for 1 1 thereby shedding light on why is conventionally restricted to this interval surprisingly however the tsallis entropy violates the third law for q 1 finally we give a concrete example of the power of our proposed method by applying it to a paradigmatic system the one dimensional ferromagnetic ising model with nearest neighbor interactions

on q gaussians and exchangeability the q gaussian distributions introduced by tsallis are discussed from the point of view of variance mixtures of normals and exchangeability for each there is a q gaussian distribution that maximizes the tsallis entropy under suitable constraints this paper shows that q gaussian random variables can be represented as variance mixtures of normals when q 1 these variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables thereby providing a possible model that has been extensively studied in probability theory the formulation provided has the additional advantage of yielding for each q a process which is naturally the q analog of the brownian motion explicit mixing distributions for q gaussians should facilitate applications to areas such as option pricing the model might provide insight into the study of superstatistics

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

irreversible processes the generalized affinities within tsallis statistics abstract within the generalized statistical mechanics introduced recently by tsallis the generalized form of the affinities the quantities which drive a process in the theory of irreversible thermodynamics was derived the affinities were obtained by considering changes in the generalized entropy s q aub of a system composed by two subsystems a and b the non extensive character of the tsallis entropy is taken into account at the end the equilibrium condition is discussed and the zeroth law in the framework of the generalized thermodynamics is consistently recovered as in the usual case two systems which are in equilibrium with a third one are necessarily in equilibrium among them and share the same temperature

the perturbative approach to path integrals a succinct mathematical treatment we study finite dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory this involves a proper understanding of how wick s theorem allows one to evaluate integrals perturbatively i e as a series expansion in a formal parameter irrespective of convergence properties we establish invariance properties of such a wick expansion under coordinate changes and the action of a lie group of symmetries and we use this to study essential features of path integral manipulations including coordinate changes ward identities schwinger dyson equations faddeev popov gauge fixing and eliminating fields by their equation of motion we also discuss the asymptotic nature of the wick expansion and the implications this has for defining path integrals perturbatively and nonperturbatively

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

roundoff induced attractors and reversibility in conservative two dimensional maps we numerically study two conservative two dimensional maps namely the baker map whose lyapunov exponent is known to be positive and a typical one exhibiting a vanishing lyapunov exponent chosen from the generalized shift family of maps introduced by c moore phys rev lett 64 1990 2354 in the context of undecidability we calculate the time evolution of the entropy sq 1 i 1wpiq q 1 s1 sbg i 1wpilnpi we exhibit the dramatic effect introduced by numerical precision indeed in spite of being area preserving maps they present well after the initially concentrated ensemble has spread virtually all over the phase space unexpected pseudo attractors fixed point like for the baker map and more complex structures for the moore map these pseudo attractors and the apparent time partial reversibility they provoke gradually disappear for increasingly large precision in the case of the moore map they are related to zero lebesgue measure effects associated with the frontiers existing in the definition of the map in addition to the above and consistent with the results by v latora and m baranger phys rev lett 82 1999 520 we find that the rate of the far from equilibrium entropy production of baker map numerically coincides with the standard kolmogorov sinai entropy of this strongly chaotic system

a tsallis statistics based neural network model for novel word learning abstract we invoke the tsallis entropy formalism a nonextensive entropy measure to include some degree of non locality in a neural network that is used for simulation of novel word learning in adults a generalization of the gradient descent dynamics realized via nonextensive cost functions is used as a learning rule in a simple perceptron the model is first investigated for general properties and then tested against the empirical data gathered from simple memorization experiments involving two populations of linguistically different subjects numerical solutions of the model equations corresponded to the measured performance states of human learners in particular we found that the memorization tasks were executed with rather small but population specific amounts of nonextensivity quantified by the entropic index q our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems