Related papers: Statistical mechanics characterization of spatio-c…
Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system. These superposition measures can be regarded as analogues to entanglement…
We investigate the critical behavior of continuous phase transitions in the context of Ginzburg Landau models with a double well effective potential. In particular, we show that the recently proposed configurational entropy, a measure of…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
Ever since Claude Shannon used entropy for his "Mathematical Theory of Communication", entropy has become a buzzword in research circles with scientists applying entropy to describe any phenomena that are reminiscent of disorder. In this…
We consider a class of endomorphisms that contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. Our goal is to study a class of endomorphisms that preserve a foliation that is almost…
Heterogeneity is classified in five categories---topologic, geometric, kinematic, static, and constitutive---and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
Hyperuniform states of matter exhibit unusual suppression of density fluctuations at large scales, contrasting sharply with typical disordered configurations. Various types of hyperuniformity emerge in multicomponent disordered systems,…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
Numerical methods for the description of nonequilibrium many-particle quantum systems such as equation of motion techniques often cannot compute the full statistics of observables but only moments of it, such as mean, variance and…
Multi-parameter statistical models may depend only on some functions of the parameters that are fewer than the number of initial parameters themselves. Such \emph{sloppy} statistical models are characterized by a degenerate Fisher…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for…
The main concern of this paper is how to define proper measures of multipartite entanglement for mixed quantum states. Since the structure of partial separability and multipartite entanglement is getting complicated if the number of…
The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell follows the steepest descending gradient toward a stable equilibrium state which represents the final cell type. It…