Related papers: Statistical mechanics characterization of spatio-c…
Detection of material inhomogeneities is an important task in magnetic imaging and plays a significant role in understanding physical processes. For example, in spintronics, the sample heterogeneity determines the onset of current-driven…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
In this paper, we investigate the relationship between chaos and homoclinic orbits from a quantitative perspective. Let f be a C^r diffeomorphism (r > 1) on a compact Riemannian manifold preserving an ergodic hyperbolic measure. We show…
A general method is presented for modeling high entropy alloys as ensembles of randomly sampled, ordered configurations on a given lattice. Statistical mechanics is applied post hoc to derive the ensemble properties as a function of…
In this Rapid Research Note the application of recently introduced [Physica A 277 (2000) 157] entropic measure S_Delta of spatial disorder for systems of finite-sized objects is presented. In the thermodynamic limit the critical behaviour…
This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=\bigtriangleup x_i\bigtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured information of a…
We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently…
Computing the electronic structure of incommensurate materials is a central challenge in condensed matter physics, requiring efficient ways to approximate spectral quantities such as the density of states (DoS). In this paper, we…
Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers etc., can be considered as ``chaotic'' superpositions of mean-field basis states (Slater determinants, products of…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here, we…
Exponential stochastic compression is the process when every second cell of an infinite chain may increase its weight merging randomly with left, right, or both neighboring cells. The total mass conservation is assumed. After that, merged…
Nonparametric rank tests for homogeneity and component independence are proposed, which are based on data compressors. For homogeneity testing the idea is to compress the binary string obtained by ordering the two joint samples and writing…