Related papers: On variational principles for metric mean dimensio…

Given a compact smooth boundaryless manifold with dimension greater than one endowed with a locally positive non-atomic measure $\mu$, we prove that typical $\mu$-preserving homeomorphisms have upper metric mean dimension, with respect to…

Let $\pi:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted…

The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of…

We introduce the mean topological dimension for random bundle transformations, and show that continuous bundle random dynamical systems with finite topological entropy, or the small boundary property have zero mean topological dimensions.

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.

In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d<x>-<dx>) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized…

In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the…

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…

We study in details the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko for a large class of densities on $\mathbb{R}^d$. We then use the work of Bickel and Breiman to prove a central limit theorem in…

We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a…

MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the…

We examine the total mixed scalar curvature of a fixed distribution as a functional of a pseudo-Riemannian metric. We develop variational formulas for quantities of extrinsic geometry of the distribution to find the critical points of this…

The recent researches in non equilibrium and far from equilibrium systems have been proved to be useful for their applications in different disciplines and many subjects. A general principle to approach all these phenomena with a unique…

We consider finite point subsets (distributions) in compact metric spaces. Non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given in the case of general…

We introduce a novel generalization of entropy and conditional entropy from which most definitions from the literature can be derived as particular cases. Within this general framework, we investigate the problem of designing…

It is argued that, for strongly non-linear behaviors, a fully deterministic position can hardly be maintained in the micro-macro transitions. This is due to the lack of information on the relevant boundary conditions, and to the tendency of…

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…

This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable Systems", by the same authors.