Related papers: Information geometry and Frobenius algebra

In this pedagogical lecture, I introduce some of the basic terminology and description of fluctuating fields as they occur on cosmology. I define various statistical, cosmological and sample homogeneity and explain what is meant by the fair…

A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical…

In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…

We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…

In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum…

We make a generalization of a self-consistent first-order perturbation scheme, being suitable for all (sub-horizon and super-horizon) scales, which has been recently constructed for the concordance cosmological model and discrete…

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a…

We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle,…

We analyse a supersymmetric mechanical model derived from (1+1)-dimensional field theory with Yukawa interaction, assuming that all physical variables take their values in a Grassmann algebra B. Utilizing the symmetries of the model we…

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…

In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge-Yukawa coupling…

Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics…

Accessible information, which is a basic quantity in quantum information theory, is computed for a general quantum Gaussian ensemble under certain "threshold condition". It is shown that the maximizing measurement is Gaussian, constituting…

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69…

I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…

Using a yukawa type of metric we derive the kretschmann scalar for a general static black hole of a certain mass. The scalar gives the curvature of the space time as a function of the radial distance in the vicinity as well as inside of the…

In Riemannian geometry geodesics are integral curves of the Riemannian distance gradient. We extend this classical result to the framework of Information Geometry. In particular, we prove that the rays of level-sets defined by a…

A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can…

In the Part I of this work we show that Friedmann equations and the thermodynamical Gibbs-Duhem relation determine a general form of the Hubble function called Model E which predicts a dynamical Dark Energy and Dark Matter with equations of…

We study a universe filled with cold dark matter in the form of discrete inhomogeneities (e.g., galaxies) and dark energy in the form of a continuous perfect fluid. We develop a first-order scalar perturbation theory in the weak gravity…