Related papers: On variational principles for metric mean dimensio…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
In this paper, we consider a dynamical system on the Riemann sphere that evolves through a set-valued map, namely a holomorphic correspondence. Analogous to the investigation of the dynamics effected by a continuous map defined on a compact…
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…
We pursue a systematic treatment of the variational capacity on metric spaces and give full proofs of its basic properties. A novelty is that we study it with respect to nonopen sets, which is important for Dirichlet and obstacle problems…
In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved…
It is widely known that when $X$ is compact Hausdorff, and when $T: X \to X$ and $f: X \to \mathbb{R}$ are continuous, \begin{equation*} P(T,f) = \sup_{\text{$\mu$: Radon probability}} \left( h_\mu(T) + \int f\, \mathrm{d}\mu \right),…
We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
We propose a metriplectic reformulation of Lagrangian variational formulations for non-equilibrium thermodynamics. We prove that solutions to these constrained variational principles can be generated by the sum of a classic Poisson bracket…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
Given a function $f\in L^2(\mathbb R)$, we consider means and variances associated to $f$ and its Fourier transform $\hat{f}$, and explore their relations with the Wigner transform $W(f)$, obtaining a simple new proof of Shapiro's…
We give an overview of some applications of a general variational principle.
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…