Related papers: Entropy of continuous mixtures and the measure pro…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
Problem of classification of all the set of entangled states is considered. Invariance of entangled states relative to transformations from a group of symmetry of qubit space leads to classification of all states of the system through…
A method has been found to analyze Edwards' granular contact force probability functional for a special case. As a result, the granular contact force probability density functions are obtained from first principles for this case. The…
We propose a mixedness quantifier based on entropy fluctuations. It provides information about the degree of mixedness either for finite dimensional and infinite dimensional Hilbert spaces. It may be used to determine the reduction of the…
Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a…
Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the…
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…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the…
Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian "hot colloids", the breakdown of detailed balance yields a…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
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…
It is assumed that in a measurement the system under study interacts with a macroscopic measuring apparatus, in such a way that the density matrix of the measured system evolves according to the Lindblad equation. Under an assumption of…
The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…