相关论文: Entropic nonextensivity as a measure of time serie…
A time series is uniquely represented by its geometric shape, which also carries information. A time series can be modelled as the trajectory of a particle moving in a force field with one degree of freedom. The force acting on the particle…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…
In the last three decades, several measures of complexity have been proposed. Up to this point, most of such measures have only been developed for finite spaces. In these scenarios the baseline distribution is uniform. This makes sense…
We demonstrate and discuss the process of gaining information and show an example in which some specific way of gaining information about an object results in the Tsallis form of entropy rather than in the Shannon one.
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics.…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
We propose a measure of learning efficiency for non-finite state spaces. We characterize the complexity of a learning problem by the metric entropy of its state space. We then describe how learning efficiency is determined by this measure…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…