相关论文: Information Geometry, One, Two, Three (and Four)

Phase transitions abound in nature and society, and, from species extinction to stock market collapse, their prediction is of widespread importance. In earlier work we showed that Global Transfer Entropy, a general measure of information…

Two types of information entropy are studied for the quantum states of a model for the matter core inside a black hole geometry. A detailed description is first given of the quantum mechanical picture leading to a spectrum of bound states…

Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…

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…

Quantum Geometry (the modern Loop Quantum Gravity using graphs and spin-networks instead of the loops) provides microscopic degrees of freedom that account for the black-hole entropy. However, the procedure for state counting used in the…

Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…

The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…

Assuming the minimal time to send a bit of information in the Einstein clock synchronization of the two clocks located at different positions, we introduce the extended metric to the information space. This modification of relativity…

Information-theoretic quantities, such as entropy, are used to quantify the amount of information a given variable provides. Entropies can be used together to compute the mutual information, which quantifies the amount of information two…

Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a…

Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…

Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of…

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…

We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $\alpha$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic…

Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested…

When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…

We study the approach to equilibrium of systems of gas particles in terms of relative entropy. The systems are modeled by the Kac master equation in arbitrary dimensions. First, we study the Kac system coupled to a thermostat, and secondly…

Inference and learning are commonly cast in terms of optimisation, yet the fundamental constraints governing uncertainty reduction remain unclear. This work presents a first-principles framework inherent to Bayesian updating, termed…

Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…