Related papers: Information geometry in vapour-liquid equilibrium
A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric…
We study the geometry of the space of densities $\VolM$, which is the quotient space $\Diff(M)/\Diff_\mu(M)$ of the diffeomorphism group of a compact manifold $M$ by the subgroup of volume-preserving diffemorphisms, endowed with a…
Results by van der Vaart (1991) from semi-parametric statistics about the existence of a non-zero Fisher information are reviewed in an infinite-dimensional non-linear Gaussian regression setting. Information-theoretically optimal inference…
We present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre…
The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…
We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>.…
In this article we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing…
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the K\"ahler manifold case. We find conditions for the information geometry of linear systems to be…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
Three-dimensional point clouds provide highly accurate digital representations of objects, essential for applications in computer graphics, photogrammetry, computer vision, and robotics. However, comparing point clouds faces significant…
The statistical properties of physical systems in thermal equilibrium are blatantly different from their far-from-equilibrium counterparts. In the latter, fluctuations often dominate the dynamics and might cluster in ordered patterns in the…
We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including non-ideal and open systems. For this purpose, we explicitly construct dual affine coordinate…
For a fissured medium, we analyze the impact that the geometry of the cracks, has in the phenomenon of preferential fluid flow. Using finite volume meshes we analyze the mechanical energy dissipation due to gravity, curvature of the surface…
Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…
We study the deformation of a liquid interface with arbitrary principal curvatures by a flat circular sheet. Working first at small slopes, we determine the shape of the sheet analytically in the membrane limit, where the sheet is…
From the perspective of the network theory, the present work illustrates how the parametric intrinsic geometric description exhibits an exact set of pair correction functions and global correlation volume with and without the inclusion of…
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…
The generalized van der Waals equation of state for anisotropic liquids in porous media consists of two terms.One of them is based on the equation of state for hard spherocylinders in random porous media obtained from the scaled particle…
Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is…
We develop a geometric formalism suited for describing the quantum thermodynamics of a certain class of nanoscale systems (whose density matrix is expressible in the McLennan--Zubarev form) at any arbitrary non-equilibrium steady state. It…