Related papers: Uniform Tests and Algorithmic Thermodynamic Entrop…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Many theoretical expressions of dissipation along non-equilibrium processes have been proposed. However, they have not been fully verified by experiments. Especially for systems strongly interacting with environments the connection between…
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
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…
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…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…
The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on groups. It is strict if and only if the random walk does not behave like the uniform measure on balls. We prove that, in any nonelementary…
Measurements can be viewed as interactions between a measured system and a pointer system that imprint information about the system on the pointer. For so-called unbiased interactions, the measurement statistics--the information…
From thermodynamics point of view, in this era of aiming at energy conservation and sustainability, we need to develop more accurate ways to design thermal power, cooling and heat pump cycles. It has been the general practice in…
Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
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…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
When the difference between changes in energy and entropy at a given temperature is correlated with the ratio between the same changes in energy and entropy at zero average free energy of an ensemble of similar but distinct molecule-sized…
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…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…