Crystallographic complexity partition analysis

We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.

Copper macrocyclic complex with trans-di[benzo]-porphyrazine and two oxo ligands: DFT quantum-chemical design

Based on the results of a quantum chemical calculation using the DFT method in the OPBE/TZVP and B3PW91/TZVP, the possibility of the existence of a copper heteroligand complex with trans-di[benzo]derivative of 3,7,11,15-tetraazaporphine (trans-di[benzo]porphyrazine) and two oxygen (O[Formula: see text] ions that is still unknown for this element was shown. In addition, the data on the structural parameters, the multiplicity of the ground state, NBO analysis and standard thermodynamic parameters of formation (standard enthalpy [Formula: see text], entropy [Formula: see text] and Gibbs’s energy [Formula: see text] for this complex are presented.

Smoothness of stable holonomies inside center-stable manifolds

Under a suitable bunching condition, we establish that stable holonomies inside center-stable manifolds for $C^{1+\beta }$ diffeomorphisms are uniformly bi-Lipschitz and, in fact, $C^{1+\mathrm {H\ddot{o}lder}}$ . This verifies the ergodicity of suitably center-bunched, essentially accessible, partially hyperbolic $C^{1+\beta }$ diffeomorphisms and verifies that the Ledrappier–Young entropy formula holds for $C^{1+\beta }$ diffeomorphisms of compact manifolds.

Social psyche and closed communicative streams as macro- and microcharacteristics of the military personnel state

In this article, the object of research is the military personnel as a system, and the subject of research is the synergetic property of the system, namely the social psyche. The main objective of the study is to quantitatively describe the system microstatuses (the number of system elements, the maximum number of servicemen included in closed separate communication streams, the total number of these streams). At the macrolevel, a measure of the statistical uncertainty of the social psyche is calculated as a synergistic property of the system. The sociometry method (D.L. Moreno), graph theory and the algorithm for calculating Hamiltonian paths (N. Christophides) are used to identify any military personnel included in closed communication streams. Boltzmann's method of calculating the entropy is used as the initial entropy formula. As a result of the study, recommendations are obtained for restructuring the leadership style, using the tendencies towards organization and disorganization in the personnel making. The novelty of the article lies in formulating the problem of determining the measure of the statistical uncertainty of the social psyche, in proving the significance of the natural scientific approach in describing and identifying the elements of the system (military personnel) and in the quantitative description of the synergetic phenomena of a social group.

The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates

This paper shows that, for a large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the W microstates of the famous Boltzmann–Planck entropy formula S = k log(W) is proved by the Shannon–McMillan theorem, a cornerstone of information theory. This result further strengthens the link between information theory and statistical mechanics.

The first law of heterotic stringy black hole mechanics at zeroth order in α′

We prove the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in α′, using Wald’s formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. We study explicitly a non-extremal, charged, black ring solution of pure $$ \mathcal{N} $$ N = 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory.This work is a first step towards the derivation of the first law at first order in α′ where, more complicated, non-Abelian, Lorentz (“gravitational”) and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.

Erratum to: T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

A correction to this paper has been published: https://doi.org/10.1007/JHEP10(2020)097