Related papers: Entropy Multiparticle Correlation Expansion for a …
Crystallization is a process of great practical relevance in which rare but crucial fluctuations lead to the formation of a solid phase starting from the liquid. Like in all first order first transitions there is an interplay between…
Classical particle systems characterized by continuous size polydispersity, such as colloidal materials, are not straightforwardly described using statistical mechanics, since fundamental issues may arise from particle distinguishability.…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure.…
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…
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…
The connection between Tsallis entropy for a multifractal distribution and Jackson's $q$-derivative is established. Based on this derivation and definition of a homogeneous function, a $q$-analogue of Shannon's entropy is discussed.…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to…
Systems of hard shapes crystallize due to entropy. How is entropy distributed among translational and rotational microscopic contributions? We answer this question by decomposing thermal fluctuation of crystals of hard hexagons into…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
Entropy or information is a fundamental quantity contained in a system in statistical mechanics and information theory. In this paper, a definition of classical information entropy of parton distribution functions is suggested. The…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based…
We prove a proposition that the entropy of the system composed of finite $N$ molecules of ideal gas is the $q$-entropy or Havrda-Charv\'at-Tsallis entropy, which is also known as Tsallis entropy, with the entropic index…