Related papers: The Information Geometry of Space-time
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should…
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the…
We propose an uncertainty relation of space-time. This relation is characterized by GhT \lesssim \delta V, where T and \delta V denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give…
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…
The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…
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…
We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two different definitions…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant…
S. Donaldson introduced a metric on the space of volume forms, with fixed total volume on any compact Riemmanian manifold. With this metric, the space of volume forms formally has non-positive curvature. The geodesic equation is a fully…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of spacetime becomes an emergent structure, which emerges from some purely…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
In the late 1990s, observations of type Ia supernovae led to the astounding discovery that the universe is expanding at an accelerating rate. The explanation of this anomalous acceleration has been one of the great problems in physics since…
In four space-time dimensions General Relativity can be non-trivially deformed. Deformed theories continue to describe two propagating degrees of freedom, as GR. We study Euclidean black hole thermodynamics in these deformations. We use the…
Since the early days of the theory of electromagnetism and of gravity the idea of space, then space-time, as a sort of physical continuum hovered the scientific community. Actually general relativity shows the strong similarity that exists…
Due to quantum fluctuations, spacetime is foamy on small scales. For maximum spatial resolution of the geometry of spacetime, the holographic model of spacetime foam stipulates that the uncertainty or fluctuation of distance $l$ is given,…
We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…