相关论文: Convergence to Stable Laws in Relative Entropy

In this paper we prove that the so--called entropy equation, i.e., \[ H\left(x, y, z\right)=H\left(x+y, 0, z\right)+H\left(x, y, 0\right) \] is stable in the sense of Hyers and Ulam on the positive cone of $\mathbb{R}^{3}$, assuming that…

We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…

In this paper, we introduce and study unified $(r,s)$-relative entropy and quantum unified $(r,s)$-relative entropy, in particular, our main results of quantum unified $(r,s)$-relative entropy are established on the separable complex…

The aim of this work is to study the role of relative entropy in the thermodynamics of black holes and cosmological horizons. We adapt some recent results on the relative entropy of coherent excitations of the vacuum, to find the variation…

A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is…

The principle of convergence stability for geometric flows is the combination of the continuous dependence of the flow on initial conditions, with the stability of fixed points. It implies that if the flow from an initial state $g_0$ exists…

The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium…

We give a short and elementary proof of stability for strong solutions of the spatially homogeneous Landau equation with Coulomb collisions, measured in relative entropy. The argument yields an explicit differential inequality for relative…

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the…

Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…

*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…

Convergence rate estimates in limit theorems for sums of independent random variables are considered.

The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…

Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $\rho$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space…

The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…

Let $\bX=\{X_n\}_{n\geq 1}$ and $\bY=\{Y_n\}_{n\geq 1}$ be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized sums $$ \psi_n(\bX,\bY)=\sum_{i=1}^nX_iY_i/V_n,\quad…

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong $L^p$-convergence version and a strongly quasi sure…