on the membership of hankel operators in a class of lorentz ideals abstract recall that the lorentz ideal c p is the collection of operators a satisfying the condition a p j 1 j p 1 p s j a consider hankel operators h f h 2 s l 2 s d h 2 s where h 2 s is the hardy space on the unit sphere s in c n in this paper we characterize the membership h f c p 2 n p

bounded functions of vanishing mean oscillation on compact metric spaces abstract a well known theorem of wolff duke math j 49 1982 321 asserts that for every f l on the unit circle t there is a non trivial q qa vmo h such that fq qc in this paper we consider the situation where t is replaced by a compact metric space x d equipped with a measure satisfying the condition b x 2 r c b x r we generalize wolff s theorem to the extent that every function in l x can be multiplied into vmo x d in a non trivial way by a function in vmo x d l x wolff s proof relies on the fact that t has a dyadic decomposition but since this is not available for x d in general our approach is completely different furthermore we show that the analyticity requirement for the function q in wolff s theorem must be dropped if t is replaced by s 2 n 1 with n 2 move precisely if n 2 then there is a g l s 2 n 1 where is the standard spherical measure on s 2 n 1 such that if q h s 2 n 1 and if q is not the constant function 0 then gq does not have vanishing mean oscillation on s 2 n 1 the particular g that we construct also serves to show that a famous factorization theorem of axler ann of math 106 1977 567 for l functions on the unit circle t cannot be generalized to s 2 n 1 when n 2 we conclude the paper with an index theorem for toeplitz operators on s 2 n 1

deriving partition functions and entropic functionals from thermodynamics abstract given an arbitrary probability distribution and a nondegenerate energy spectrum so that a mean energy u can be computed we derive the partition function z and the entropic functional s that satisfy the basic relation d u t d s the procedure is illustrated by considering examples of typical distributions found currently in nature in particular the power law spectrum is shown to correspond to a critical state associated with tsallis entropy

boundedness and compactness of hankel operators on the sphere abstract we consider hankel operators on the hardy space of the unit sphere in c n we show that a large amount of information about the function f p f can be recovered from the hankel operator h f for example if h f is compact then the function f p f is necessarily in vmo

a unified characterization of generalized information and certainty measures abstract in this paper we consider the axiomatic characterization of information and certainty measures in a unified way we present the general axiomatic system which captures the common properties of a large number of the measures previously considered by numerous authors we provide the corresponding characterization theorems and define a new generalized measure called the inforcer which is the quasi linear mean of the function associated with the event probability following the general composition law in particular we pay attention to the polynomial composition and the corresponding polynomially composable inforcer measure the most common measures appearing in literature can be obtained by specific choice of parameters appearing in our generic measure and they are listed in tables

generalized shannon khinchin axioms and uniqueness theorem for pseudo additive entropies abstract we consider the shannon khinchin axiomatic systems for the characterization of generalized entropies such as the sharma mittal and frank daffertshofer entropies we provide the generalization of the shannon khinchin axioms and give the corresponding uniqueness theorem the previous attempts at such axiomatizations are also discussed

deformed exponentials and logarithms in generalized thermostatistics abstract criteria are given that deformed logarithmic and exponential functions should satisfy with a pair of such functions one can associate another function called the deduced logarithmic function it is shown that generalized thermostatistics can be formulated in terms of deformed exponential functions together with the associated deduced logarithmic functions

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

superstatistics thermodynamics and fluctuations a thermodynamiclike formalism is developed for superstatistical systems based on conditional entropies this theory takes into account large scale variations of intensive variables of systems in nonequilibrium stationary states ordinary thermodynamics is recovered as a special case of the present theory and corrections to it can systematically be evaluated a generalization of einstein s relation for fluctuations is presented using a maximum entropy condition

schatten class membership of hankel operators on the unit sphere abstract let h 2 s be the hardy space on the unit sphere s in c n n 2 consider the hankel operator h f 1 p m f h 2 s where the symbol function f is allowed to be arbitrary in l 2 s d we show that for p 2 n h f is in the schatten class c p if and only if f p f belongs to the besov space b p to be more precise the if part of this statement is easy the main result of the paper is the only if part we also show that the membership h f c 2 n implies f p f 0 i e h f 0

generalized entropies and the transformation group of superstatistics superstatistics describes statistical systems that behave like superpositions of different inverse temperatures so that the probability distribution is where the kernel f is nonnegative and normalized f d 1 we discuss the relation between this distribution and the generalized entropic form the first three shannon khinchin axioms are assumed to hold it then turns out that for a given distribution there are two different ways to construct the entropy one approach uses escort probabilities and the other does not the question of which to use must be decided empirically the two approaches are related by a duality the thermodynamic properties of the system can be quite different for the two approaches in that connection we present the transformation laws for the superstatistical distributions under macroscopic state changes the transformation group is the euclidean group in one dimension

canonical ensemble in non extensive statistical mechanics the framework of non extensive statistical mechanics proposed by tsallis has been used to describe a variety of systems the non extensive statistical mechanics is usually introduced in a formal way using the maximization of entropy in this paper we investigate the canonical ensemble in the non extensive statistical mechanics using a more traditional way by considering a small system interacting with a large reservoir via short range forces the reservoir is characterized by generalized entropy instead of the boltzmann gibbs entropy assuming equal probabilities for all available microstates we derive the equations of the non extensive statistical mechanics such a procedure can provide deeper insight into applicability of the non extensive statistics

a theorem on the existence of trace form generalized entropies an analytic technique is proposed which allows to generate many new examples of entropic functionals generalizing the standard boltzmanngibbs entropy our approach is based on the existence of a g

transition from lognormal to χ2 superstatistics for financial time series abstract share price returns on different time scales can be well modelled by a superstatistical dynamics here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales it is shown that while 2 superstatistics works well on a time scale of days on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics the system dynamics thus exhibits a transition from lognormal to 2 superstatistics as a function of time scale we discuss a more general model interpolating between both statistics which fits the observed data very well we also present results on correlation functions of the extracted superstatistical volatility parameter which exhibits exponential decay for returns on large time scales whereas for returns on small time scales there are long range correlations and power law decay

bergman commutators and norm ideals let p be the orthogonal projection from l2 b dv onto the bergman space la2 b dv of the unit ball in cn in this paper we characterize the membership of commutators of the form mf p in the norm ideal c where the symmetric gauge function is allowed to be arbitrary

generalized boltzmann factors and the maximum entropy principle entropies for complex systems abstract we generalize the usual exponential boltzmann factor to any reasonable and potentially observable distribution function b e by defining generalized logarithms as inverses of these distribution functions we are led to a generalization of the classical boltzmann gibbs entropy s bg d e e b e ln b e to the expression s d e e 0 b e d x x which contains the classical entropy as a special case we show that this is the unique modification of entropy which is compatible with the maximum entropy principle for arbitrary non exponential distribution functions we demonstrate that this entropy has two important features first it describes the correct thermodynamic relations of the system and second the observed distributions are straightforward solutions to the jaynes maximum entropy principle with the ordinary not escort constraints tsallis entropy is recovered as a further special case

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

from time series to superstatistics complex nonequilibrium systems are often effectively described by a statistics of a statistics in short a superstatistics we describe how to proceed from a given experimental time series to a superstatistical description we argue that many experimental data fall into three different universality classes chi2 superstatistics tsallis statistics chi2 inverse superstatistics and log normal superstatistics we discuss how to extract the two relevant well separated superstatistical time scales tau and t the probability density of the superstatistical parameter beta and the correlation function for beta from the experimental data we illustrate our approach by applying it to velocity time series measured in turbulent taylor couette flow which is well described by log normal superstatistics and exhibits clear time scale separation

double density dynamics realizing a joint distribution of a physical system and a parameter system to perform a variety of types of molecular dynamics simulations we created a deterministic method termed double density dynamics ddd which realizes an arbitrary distribution for both physical variables and their associated parameters simultaneously specifically we constructed an ordinary differential equation that has an invariant density relating to a joint distribution of the physical system and the parameter system a generalized density function leads to a physical system that develops under nonequilibrium environment describing superstatistics the joint distribution density of the physical system and the parameter system appears as the radon nikodym derivative of a distribution that is created by a scaled long time average generated from the flow of the differential equation under an ergodic assumption the general mathematical framework is fully discussed to address the theoretical possibility of our method and a numerical example representing a 1d harmonic oscillator is provided to validate the method being applied to the temperature parameters

incidence of q statistics in rank distributions we show that size rank distributions with power law decay often only over a limited extent observed in a vast number of instances in a widespread family of systems obey tsallis statistics the theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the lyapunov exponent is negligible or vanishes the relevant statistical mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints and the resulting duality of entropy indexes is seen to portray physically relevant information whereas the value of the index fixes the distribution s power law exponent that for the dual index 2 ensures the extensivity of the deformed entropy

generalized entropy optimized by a given arbitrary distribution an ultimate generalization of the maximum entropy principle is presented an entropic measure which is optimized by a given arbitrary distribution with the finite linear expectation value of a physical random quantity of interest is constructed it is concave irrespective of the properties of the distribution and satisfies the h theorem for the master equation combined with the principle of microscopic reversibility this offers a unified basis for a great variety of distributions observed in nature as examples the entropies associated with the stretched exponential distribution postulated by anteneodo and plastino 1999 j phys a math gen 32 1089 and the deformed exponential distribution by kaniadaki 2002 phys rev e 66 056125 and naudts 2002 physica a 316 323 are derived to include distributions with divergent moments e g the levy stable distributions it is necessary to modify the definition of the expectation value

tsallis distributions and 1 f noise from nonlinear stochastic differential equations probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems in this article we unite modeling of such distributions with the model of widespread 1 f noise we propose a class of nonlinear stochastic differential equations giving both the q exponential or q gaussian distributions of signal intensity revealing long range correlations and 1 f behavior of the power spectral density the superstatistical framework to get 1 f noise with q exponential and q gaussian distributions of the signal intensity is proposed as well

a generalized quasilinearization method for second order nonlinear differential equations with nonlinear boundary conditions we consider the differential equation l u f u where l is a formally self adjoint second order differential expression and f is nonlinear with nonlinear boundary conditions under appropriate assumptions on l f and the boundary conditions existence of solutions is established using the method of lower and upper solutions a generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation

use of the geometric mean as a statistic for the scale of the coupled gaussian distributions abstract the geometric mean is shown to be an appropriate statistic for the scale of a heavy tailed coupled gaussian distribution or equivalently the student s t distribution the coupled gaussian is a member of a family of distributions parameterized by the nonlinear statistical coupling which is the reciprocal of the degree of freedom and is proportional to fluctuations in the inverse scale of the gaussian existing estimators of the scale of the coupled gaussian have relied on estimates of the full distribution and they suffer from problems related to outliers in heavy tailed distributions in this paper the scale of a coupled gaussian is proven to be equal to the product of the generalized mean and the square root of the coupling from our numerical computations of the scales of coupled gaussians using the generalized mean of random samples it is indicated that only samples from a cauchy distribution with coupling parameter one form an unbiased estimate with diminishing variance for large samples nevertheless we also prove that the scale is a function of the geometric mean the coupling term and a harmonic number numerical experiments show that this estimator is unbiased with diminishing variance for large samples for a broad range of coupling values

transitions between superstatistical regimes validity breakdown and applications abstract superstatistics is a widely employed tool of non equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems yet its canonical formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data here we show that a multi scale generalization of the superstatistics paradigm is more versatile allowing to address such pertinent issues as transmutation of statistics or inter scale stochastic behavior to put some flesh on the bare bones we provide a numerical evidence for a transition between two superstatistics regimes by analyzing high frequency minute tick data for share price returns of seven selected companies salient issues such as breakdown of superstatistics in fractional diffusion processes or connection with brownian subordination are also briefly discussed

toeplitz operators and hankel operators on the hardy space of the unit sphere abstract a sufficient condition is found for the product of two toeplitz operators on the hardy space of the unit sphere to be a compact perturbation of a toeplitz operator the condition leads to a criterion for a hankel operator to be compact

complex networks emerging from fluctuating random graphs analytic formula for the hidden variable distribution in analogy to superstatistics which connects boltzmann gibbs statistical mechanics to its generalizations through temperature fluctuations complex networks are constructed from fluctuating erd os r enyi random graphs using a quantum mechanical method the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the poisson transformation as an example a static scale free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin

superstatistics in nanoscale electrochemical systems stochastic electrochemical reaction steps on nanosized electrodes are non markovian when externally driven by an applied voltage we show that compared to the markovian case when external driving is absent nanoscale electrochemical systems obey a superstatistics characterized by a superposition of tsallis q indices the distribution of tsallis q indices along stochastic trajectories can be calculated from the electrochemical master equation and normal distributions from boltzmann gibbs thermostatistics are recovered in the thermodynamic limit the infinite electrode size limit although on the nanoscale the external control makes intricate correlations between the microstates in the superstatistical frame one can still address the microstates as if they were uncorrelated the resulting superstatistical entropic form is additive in this frame and tsallis indices have on the time average values which is indeed an example of a superstatistical system where no ad hoc distribution has to be assumed for the fluctuations rather the distribution is directly calculated from a mesoscopic master equation without freely adjustable parameters

coupled nose hoover equations of motions without time scaling the nose hoover nh equation of motion is widely used in molecular dynamics simulations it enables us to set a constant temperature and produce the canonical distribution for a target physical system for the purpose of investigating the physical system under fluctuating temperature we have introduced a coupled nose hoover equation in our previous work fukuda and moritsugu 2015 j phys a math theor 48 455001 the coupled nh equation implements a fluctuating heat bath temperature in the nh equation of the physical system and also keeps a statistically complete description via an invariant measure of the total system composed of the physical system and a temperature system however a difficulty lies in that the time development of the physical system may not correspond to the realistic physical process because of the need of a scaled time average to compute thermodynamical quantities the current work gives a solution by presenting a new scheme which is free from the scaled time but retains the statistical description by use of simple model systems we validate the current scheme and compare with the original scheme the sampling property of the current scheme is also clarified to investigate the effect of function setting used for the distribution of the total system

analysis of human dna through power law statistics we report an analysis of homo sapiens dna through the formalism of statistics which encompasses power law correlations and provides an optimization principle that permits us to model distinct physical systems i e the power law distribution of the length of dna bases is calculated from a general model which follows arguments similar to those proposed in maxwell s deduction of statistical distributions the viability of the model is tested using a data set from a catalog of proteins collected from the ensembl project the results indicate that the short range correlations always present in coding dna sequences are appropriately captured through the kaniadakis power law distribution adequately describing the cumulative length distribution of dna bases in contrast with the case of the traditional exponential statistical model

on the average uncertainty for systems with nonlinear coupling abstract the increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function new insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions the shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities for the exponential and gaussian distributions we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale i e at the width of the distribution the average uncertainty is generalized via the weighted generalized mean in which the moment is a function of the nonlinear source both the renyi and tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain for the generalized pareto and student s t distributions which are the maximum entropy distributions for these generalized entropies the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale a coupled entropy function is proposed which is equal to the normalized tsallis entropy divided by one plus the coupling