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The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…

Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of…

Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This…

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…

Imaging systems are commonly described using resolution, contrast, and signal-to-noise ratio, but these quantities do not provide a general account of how physical transformations affect the flow of information. This paper introduces an…

The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…

Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…

Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…

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…

In this paper, we explore the entropy uncertainty for qutrit system under non-Markov noisy environment and discuss the effects of the quantum memory system and the spontaneously generated interference (SGI) on the entropy uncertainty in…

An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…

Spiking activity from populations of neurons display causal interactions and memory effects. Therefore, they are expected to show some degree of irreversibility in time. Motivated by the spike train statistics, in this paper we build a…

In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…

The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as…

In this study, we uncover the intrinsic information processes in non-Hermitian quantum systems and their thermodynamic effects. We demonstrate that these systems can exhibit negative entropy production, making them potential candidates for…

In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…

We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…

With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction…