Related papers: Information geometry in vapour-liquid equilibrium
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
Substructure in the interstellar medium (ISM) is crucial for establishing the correlation between star formation and feedback and has the capacity to significantly perturb stellar orbits, thus playing a central role in galaxy dynamics and…
We introduce the notion of smooth parametric model of normal positive linear functionals on possibly infinite-dimensional W*-algebras generalizing the notions of parametric models used in classical and quantum information geometry. We then…
We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
In this work, the van der Waals fluid model, a diffuse-interface model for liquid-vapor two-phase flows, is numerically investigated. The thermodynamic properties of the van der Waals fluid are first studied. Dimensional analysis is…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
The paper is devoted to the thermodynamics of normal surface electromagnetic fields within a nonuniform dispersive and absorptive system. This system is formed by vacuum and lossy medium separated by a plane interface. As a medium, we used…
Despite its importance in geological sciences, our understanding of interactions between gas and condensed phases (comprising solids and liquids) remains clouded by the fact that, often, only indirect evidence remains for their occurrence.…
In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information…
Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from $M$ to $\mathbb R^n$. The results of \cite{Michor118}, where mean curvature…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Theory of the first-order phase transition in contact statistical manifold has been proposed to describe interface systems. The theory has not limitations of known Van der Waals-like phase transitions theories. Based on this approach,…
Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) we can pick apart the interface structure and understand surface tension. In…
This paper studies distributed-parameter systems on Riemannian manifolds with respect to Stokes-Dirac structures in a language of contact geometry with fiber bundles. For the class where energy functionals are quadratic, it is shown that…
We advocate the use of a notion of entropy that reflects the relative abundances of the symbols in an alphabet, as well as the similarities between them. This concept was originally introduced in theoretical ecology to study the diversity…
High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures…
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…