Related papers: Entropy numbers and Marcinkiewicz-type discretizat…
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…
In this paper, we established the boundedness of m-linear Marcinkiewicz integral on Campanato type spaces. We showed that if the $m$-linear Marcinkiewicz integral is finite for one point, then it is finite almost everywhere. Moreover, the…
We describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for…
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…
The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…
Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Amp\`ere equations involving sublevel sets, and bypasses the…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Building on work of Kontsevich, we introduce a definition of the entropy of a finite probability distribution in which the "probabilities" are integers modulo a prime p. The entropy, too, is an integer mod p. Entropy mod p is shown to be…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Given a general scalar balance law, i.e., in several space dimensions and with flux and source both space and time dependent, we focus on the functional properties of the entropy production. We apply this operator to entropy solutions, to…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
The main purpose of this article is to provide a common generalization of the notions of a topological and Kolmogorov-Sinai entropy for arbitrary representations of discrete amenable groups on objects of (abstract) categories. This is…
Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
Entropy production quantifies the breaking of time-reversal symmetry in non-equilibrium systems. Here, we develop a direct method to obtain closed, tractable expressions for entropy production in a broad class of dynamical density…
An "entropy increasing to the maximum" result analogous to the entropic central limit theorem (Barron 1986; Artstein et al. 2004) is obtained in the discrete setting. This involves the thinning operation and a Poisson limit. Monotonic…