Related papers: Information geometry, simulation and complexity in…
A common way to learn and analyze statistical models is to consider operations in the model parameter space. But what happens if we optimize in the parameter space and there is no one-to-one mapping between the parameter space and the…
The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…
The time evolution of a physical system is generally described by a differential equation, which can be solved numerically by adopting a difference scheme with space-time discretization. This discretization, as a numerical artifact, results…
Understanding how neural population responses represent sensory information is a central problem in systems neuroscience. One approach is to define a representational geometry on stimulus space in which distances reflect how reliably…
We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase…
We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study,…
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the…
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for…
We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that…
We analyzed the noncommutativity effects on the Fisher information (F_(r,p)) and Shannon entropies (S_(r,p)) of a harmonic oscillator immersed in a time-varying electric field in two and three dimensions. We find the exact solutions of the…
The act of measuring a system has profound consequences of dynamical and thermodynamic nature. In particular, the degree of irreversibility ensuing from a non-equilibrium process is strongly affected by measurements aimed at acquiring…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this article, we focus on…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
Concepts of the complex partition functions and the Fisher zeros provide intrinsic statistical mechanisms for finite temperature and real time dynamical phase transitions. We extend the utility of these complexifications to quantum phase…
Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently…
For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…