Related papers: Escort mean values and the characterization of pow…
As well known, cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist. If this is not the case, the so called escort mean values (or q-moments) have been…
We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The…
The purity of Werner state in nonextensive formalism associated with two different constraints has been calculated in a previous paper by G. B. Bagci et al. [G. B. Bagci et al., Int. J. Mod. Phys. 20, 2085 (2006)]. Two different results…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
Escort distributions have been shown to be very useful in a great variety of fields ranging from information theory, nonextensive statistical mechanics till coding theory, chaos and multifractals. In this work we give the notion and the…
It is currently a widely used practice to write the constraints in terms of escort averages when the generalized entropies are employed in the maximization scheme. We show that the maximization of the nonadditive $q$-entropy with escort…
We discuss the basic transport phenomena in gases and plasmas obeying the $q$-nonextensive velocity distribution (power-law). Analytical expressions for the thermal conductivity ($K_q$) and viscosity ($\eta_q$) are derived by solving the…
We evaluate generalized information measures constructed with Husimi distributions and connect them with the Wehrl entropy, on the one hand, and with thermal uncertainty relations, on the other one. The concept of escort distribution plays…
A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian…
We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain…
We present an argument about the origin of escort distributions used in conjunction with the q-entropy in non-additive thermo-statistics. The origin of the escort distributions is ascribed to the fact that the effective statistical…
Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions…
By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is…
We study the escort probability distribution function of work done during an interaction quantum quench of Luttinger liquids. It crosses over from the thermodynamic to the small system limit with increasing $a$, the order of the escort…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only…
It was recently proven [Hilhorst, JSTAT, P10023 (2010)] that the q-generalization of the Fourier transform is not invertible in the full space of probability density functions for q > 1. It has also been recently shown that this…
The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a…
Parametrized families of density operators are studied. A generalization of the lower bound of Cramer and Rao is formulated. It involves escort density operators. The notion of phi-exponential family is introduced. This family, together…