Related papers: The Frieden-Soffer Extreme Physical Information Pr…
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
The porous media equation has been proposed as a phenomenological ``non-extensive'' generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming…
In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet-Neumann boundary data which extends the one proved by J. D\'avila to the fractional setting. In particular, we present a comparison…
"Information is physical", and here we consider the physical directional information of a particle with spin. We ask whether, in the presence of a classical frame of reference, such a particle contains any intrinsic directional information,…
The free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment. In this work, we examine in depth the assumptions required to derive the FEP in the…
The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…
Data-driven approaches coupled with physical knowledge are powerful techniques to model systems. The goal of such models is to efficiently solve for the underlying field by combining measurements with known physical laws. As many systems…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
We establish two Phragm\'en--Lindel\"{o}f theorems for a fully nonlinear elliptic equation. We consider a dynamic boundary condition that includes both spatial variable and time derivative terms. As a spatial term, we consider a non-linear…
We considered classical solutions to the initial boundary value problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We obtained global a priori estimates and global existence results of classical…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
The inverse Stefan problem, as a typical phase-change problem with moving boundaries, finds extensive applications in science and engineering. Recent years have seen the applications of physics-informed neural networks (PINNs) to solving…
We study the principle of information causality for the set of extremal correlations in the tripartite scenario. We show that all but one nonlocal extremal correlations in this scenario violate information causality. This undetected…
To explain conceptual gap between classical/quantum and other, hypothetical descriptions of world, several principles has been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm uses a maximum information principle to select from among the…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…