Related papers: Measurement Invariance, Entropy, and Probability
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
In this paper, we study the generic action for the scale-invariant theory of gravity and then by making use of the holographic methods, we compute some specific holographic measures of entanglement. Precisely, we calculate the entanglement…
The use of coarse graining to connect physical and information theoretic entropies has recently been given a precise formulation in terms of ``observational entropy'', describing entropy for observers with respect to a measurement. Here we…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and…
We study samples of natural images for which a set of statistical characteristics is computed and scale-invariant properties of samples are demonstrated computationally. Computations of the power spectrum are carried out and a power-law…
We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The result of a physical measurement depends on the timescale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to…
The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities…
We investigate multiscale Gibbs measures from a variational and probabilistic viewpoint, focusing on the structural asymmetry among conditional entropies that characterizes their construction. We show how this asymmetry emerges both from…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
Measurement-driven transitions between extensive and sub-extensive scaling of the entanglement entropy receive interest as they illuminate the intricate physics of thermalization and control in open interacting quantum systems. Whilst this…
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…
We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…
The majorizing measure theorem of Fernique and Talagrand is a fundamental result in the theory of random processes. It relates the boundedness of random processes indexed by elements of a metric space to complexity measures arising from…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…