Related papers: Information geometry in vapour-liquid equilibrium
Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…
We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic…
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…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
A novel information-geometrodynamical approach to chaotic dynamics (IGAC) on curved statistical manifolds based on Entropic Dynamics (ED) is presented and a new definition of information geometrodynamical entropy (IGE) as a measure of…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
This paper explores the Bergman geometry of bounded domains $\Omega$ in $\mathbb{C}^n$ through the lens of information geometry by introducing a mapping $\Phi: \Omega \rightarrow \mathcal{P}(\Omega)$, where $\mathcal{P}(\Omega)$ denotes a…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It…
In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is…
We find the information geometry of tempered stable processes. Beginning with the derivation of $\alpha$-divergence between two tempered stable processes, we obtain the corresponding Fisher information matrices and the $\alpha$-connections…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
A new information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s}…
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We…
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
Differential geometry is powerful tool to analyze the vapor-liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point $\left( \partial p/\partial V\right) _{T}=0$…
In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical…
Models of bounded rationality include quantum--like (QL) models, which use Hilbert--space amplitudes to represent context and order effects, and entropy--regularised (ER) models, including rational inattention, which smooth expected utility…
In problems of parameter estimation from sensor data, the Fisher Information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the…