相关论文: Generalized Entropy Method for the Renewal Equatio…

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…

Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods.…

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…

Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…

To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of…

Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we show that the entropy map of an expanding…

This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…

The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…

An alternative method is presented for extracting the von Neumann entropy $-\operatorname{Tr} (\rho \ln \rho)$ from $\operatorname{Tr} (\rho^n)$ for integer $n$ in a quantum system with density matrix $\rho$. Instead of relying on direct…

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…

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective…

To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different…

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects…

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…

We prove the following asymptotic behavior for solutions to the generalized Becker-D\"oring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical…

We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…

We establish sharp long time asymptotic behaviour for a family of entropies to defective Fokker-Planck equations and show that, much like defective finite dimensional ODEs, their decay rate is an exponential multiplied by a polynomial in…

Traditional measures of entropy, like the Von Neumann entropy, while fundamental in quantum information theory, are insufficient when interpreted as thermodynamic entropy due to their invariance under unitary transformations, which…