Related papers: Deformed Tsallis-statistics analysis of a complex …
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
Within Tsallis' nonextensive statistics, a model is elaborated to address self-similar time series as a thermodynamic system. Thermodynamic-type characteristics relevant to temperature, pressure, entropy, internal and free energies are…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We study information measures in quantu mechanics, with particular emphasis on providing a quantification of the notions of classicality and predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a precise criterion for…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic…
The optimization problems defining meta-stable or stationary equilibrium are explored. The Gibbs scheme is modified aiming to describe the statistical properties of a class of non-equilibrium and metastable states. The system is assumed to…
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to…
This study investigates the dynamics of quantum information and computational resources using a tractable model of coupled harmonic oscillators. We precisely characterize the interplay between mutual information, synchronization, and…
We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean field evolution. This…
We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…