The authors introduce a novel entropic notion with the purpose of quantifying disorder/uncertainty in networks. This is based on the Laplacian and it is exactly the von Neumann entropy of certain quantum mechanical states. It is remarkable that the von Neumann entropy depends on spectral properties and it can be computed efficiently. The analytical results described here and the numerical compu...

Among the normalized metrics on a graph, we show the existence and the uniqueness of an entropy-minimizing metric, and give explicit formulas for the minimal volume entropy and the metric realizing it. Parmi les distances normalisées sur un graphe, nous montrons l’existence et l’unicité d’une distance qui minimise l’entropie, et nous donnons des formules explicites pour l’entropie volumique min...

Contents 1. Introduction 1 2. Ergodic theory: some background 4 3. Entropy of dynamical systems: some more background 6 4. Conditional Expectation and Martingale theorems 12 5. Countably generated σ-algebras and Conditional measures 14 6. Leaf-wise Measures, the construction 19 7. Leaf-wise Measures and entropy 37 8. The product structure 61 9. Invariant measures and entropy for higher rank sub...

Lately, there has been some interest in modifications of the compressible Navier-Stokes equations to include diffusion of mass. In this paper, we investigate possible ways to add mass diffusion to the 1-D Navier-Stokes equations without violating the basic entropy inequality. As a result, we recover a general form of Brenner’s modification of the Navier-Stokes equations. We consider Brenner’s s...

The thermodynamic functions such as enthalpy (H), Gibbs free energy (G) and entropy (S) of Serineand Threonine amino acids were theoretically studied at different condition (solvents andtemperatures) by using Gussian o3, software. First, the structural optimization of isolated Serine andThreonine were done in the gas phase by using the Hartree-Fock (HF) level of theory with 3-21G, 6-31G and 6-3...

We study slow entropy invariants for abelian unipotent actions $ U on any finite volume homogeneous space G/\Gamma $. For every such action we show that the topological can be computed directly from dimension of a special decomposition {{\rm{Lie}}}(G) induced by {{\rm{Lie}}}(U) Moreover, are able to metric coincides with its entropy. As corollary, obtain complexity horocyclic is only related G ...

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure with respect to a continuous and regular g-function. We prove large deviation principles for conditional, non-conditional an...

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set G the ε-entropy (per unit length) exists in the topology of W 1,∞. We also show that the topological entropy per unit length of G exists. These results are shown using two main techniques: Bounds in bounded domains in position space and for large momenta, and a novel submultiplicativity argument...