相关论文: Fluctuation geometry: A counterpart approach of in…
Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from…
We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…
This essay fuses concepts and approaches used to describe fluctuating phenomena in climate systems and statistical mechanics, and explores new ideas essential for understanding such phenomena. Its starting points are the Langevin equation…
Based on a generalized local Kolmogorov-Hill equation expressing the evolution of kinetic energy integrated over spheres of size $\ell$ in the inertial range of fluid turbulence, we examine a possible definition of entropy and entropy…
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a…
We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time…
Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the…
Entanglement fluctuations associated with Schr\"{o}dinger evolution of wavefunctions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a…
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…
The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The…
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…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Adopting the Landau-Lifshiftz method of classical fluctuations we determine the statistical average strength of the fluctuations of the energy flux on the apparent horizon of a homogeneous and isotropic universe described by Einstein…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in…
The irreversibility of trajectories in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. We consider stochastic maps resulting from a time discretization with interval \tau…
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…