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Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this…

Quantum Physics · Physics 2016-11-02 Jamie Sikora , Antonios Varvitsiotis , Zhaohui Wei

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

Analysis of PDEs · Mathematics 2017-10-11 E. S. Daus , L. Desvillettes , A. Jüngel

A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…

Information Theory · Computer Science 2007-07-13 Joseph DeStefano , Erik Learned-Miller

We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…

Quantum Physics · Physics 2025-03-04 Mario Berta , Ludovico Lami , Marco Tomamichel

An overview of recent advances in the theory of critical phenomena in $d$-dimensional weakly anisotropic systems is given. On the basis of a generalized shear transformation between anisotropic and isotropic systems, exact and approximate…

Statistical Mechanics · Physics 2023-11-07 Volker Dohm

Bounding and estimating entropy production has long been an important goal of nonequilibrium thermodynamics. We recently derived a lower bound on the total and subsystem entropy production rates of continuous stochastic systems. This…

Statistical Mechanics · Physics 2024-02-29 Matthew P. Leighton , David A. Sivak

The third named author has been developing a theory of "higher" symplectic capacities. These capacities are invariant under taking products, and so are well-suited for studying the stabilized embedding problem. The aim of this note is to…

Symplectic Geometry · Mathematics 2022-02-21 Dan Cristofaro-Gardiner , Richard Hind , Kyler Siegel

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a…

Machine Learning · Computer Science 2023-01-20 Florian Graf , Sebastian Zeng , Bastian Rieck , Marc Niethammer , Roland Kwitt

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…

Dynamical Systems · Mathematics 2018-02-27 Dou Dou , Wen Huang , Kyewon Koh Park

We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…

Functional Analysis · Mathematics 2024-05-21 Thomas Allard , Helmut Bölcskei

We study thermodynamic limits when controllers operate with only partial observability of internal correlations in multipartite systems. Understanding the costs imposed by lack of information is crucial in settings where agents must act…

Statistical Mechanics · Physics 2025-09-25 Akihito Sudo

In this paper, we study two issues in asynchronous communication systems. The first issue is the derivation of sum capacity bounds for finite dimensional asynchronous systems. In addition, asymptotic results for the sum capacity bounds are…

Signal Processing · Electrical Eng. & Systems 2019-03-19 Shayan Dashmiz , Seyed Mohammad Mansouri , Amir Najafi , Farrokh Marvasti

Channel capacity bounds are derived for a point-to-point indoor visible light communications (VLC) system with signal-dependent Gaussian noise. Considering both illumination and communication, the non-negative input of VLC is constrained by…

Information Theory · Computer Science 2020-11-03 Jin-Yuan Wang , Xian-Tao Fu , Rong-Rong Lu , Jun-Bo Wang , Min Lin , Julian Cheng

Entropy production is a universal measure of irreversibility and energy dissipation in physical, chemical, and biological systems operating far from equilibrium. However, quantifying and spatiotemporally localising it in complex processes…

Statistical Mechanics · Physics 2026-05-18 Biswajit Das , Sreekanth K Manikandan

In this paper, we introduce the resource theory of unextendibility as a relaxation of the resource theory of entanglement. The free states in this resource theory are the k-extendible states, associated with the inability to extend quantum…

Quantum Physics · Physics 2021-09-07 Eneet Kaur , Siddhartha Das , Mark M. Wilde , Andreas Winter

The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…

Information Theory · Computer Science 2025-12-23 Mokshay Madiman , James Melbourne , Cyril Roberto

An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…

Quantum Physics · Physics 2024-11-01 M. E. Shirokov

This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between…

Optimization and Control · Mathematics 2018-09-11 George I. Boutselis , Marcus Pereira , Evangelos A. Theodorou

Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…

Quantum Physics · Physics 2017-08-23 M. E. Shirokov

Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external…

Statistical Mechanics · Physics 2021-11-12 Shriram Chennakesavalu , Grant M. Rotskoff