Related papers: Incomplete information and fractal phase space
The ubiquitous clumpy state of the ISM raises a fundamental and open problem of physics, which is the correct statistical treatment of systems dominated by long range interactions. A simple solvable hierarchical model is presented which…
In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…
We examine the scaling of the inverse participation ratio of spin coherent states in the energy basis of three collective spin systems: a bounded harmonic oscillator, the Lipkin-Meshkov-Glick model, and the Quantum Kicked Top. The…
The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…
A general problem of optimal information acquisition for its use in decision making problems is considered. This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
We study {\it permeable} sets. These are sets \(\Theta \subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(\gamma\) which has small (or even empty, apart from the…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Partial orders have been used to model several experimental setups, going from classical thermodynamics and general relativity to the quantum realm with its resource theories. In order to study such experimental setups, one typically…
A physical field has an infinite number of degrees of freedom since it has a field value at each location of a continuous space. Therefore, it is impossible to know a field from finite measurements alone and prior information on the field…
The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture. In this first paper we establish the mathematical foundation of a cohesive phase-field model by proving a…
The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…