Related papers: A note on characterization based on past entropy

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…

Systems driven away from thermal equilibrium constantly deliver entropy to their environment. Determining this entropy production requires detailed information about the system's internal states and dynamics. However, in most practical…

This note has been withdrawn by the author as the more complete result was recently proved by A.Quas and Y.Peres

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…

An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a…

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…

We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…

We provide a simple proof of a curious inequality for the binary entropy function, an inequality that has been used in two different contexts. In the 1980's, Boppana used this entropy inequality to prove lower bounds on Boolean formulas.…

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…

We prove in this text a characterization of the possible entropy dimensions of minimal tridimensional subshifts of finite type with a computability condition, using Goldbach's theorem on Fermat numbers.

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid…

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…

The folding entropy is a quantity originally proposed by Ruelle in 1996 during the study of entropy production in the non-equilibrium statistical mechanics. As derived through a limiting process to the non-equilibrium steady state, the…

There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

We establish an exact identity for overdamped Langevin dynamics: the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This yields…

We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…