Related papers: Incomplete information and fractal phase space
Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many…
Incompleteness theorems of Godel, Turing, Chaitin, and Algorithmic Information Theory have profound epistemological implications. Incompleteness limits our ability to ever understand every observable phenomenon in the universe.…
Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…
Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…
Dynamical system analysis of a universe model which contains matter, radiation, and quintessence with exponential potential, $V \!(\phi)=V_{\!o} \, exp(-\alpha \kappa \phi) \,$, is studied in the light of recent observations and the…
A contribution is presented to the application of fractal properties and log-periodic corrections to the masses of several nuclei (isotopes or isotones), and to the energy levels of some nuclei. The fractal parameters $\alpha$ and $\lambda$…
The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the…
Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…