相关论文: Geometric partition functions of cellular systems:…

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It…

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…

Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…

In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…

Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize…

We measure different contributions to entropy production in a living functional epithelial tissue. We do this by extracting the functional dynamics of development while at the same time quantifying fluctuations. Using the translucent…

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…

A phenomenological model hamiltonian to describe the folding of a protein with any given sequence is proposed. The protein is thought of as a collection of pieces of helices; as a consequence its configuration space increases with the…

Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy…

We present numerical simulations that allow us to compute the number of ways in which $N$ particles can pack into a given volume $V$. Our technique modifies the method of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and outperforms…

We give a closed-form solution of von Neumann entropy as a function of geometric phase modulated by visibility and average distinguishability in Hilbert spaces of two and three dimensions. We show that the same type of dependence also…

We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is…

Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…

It is presented the general properties of N-dimensional multi-component or many-particle systems exhibiting self-similar hierarchical structure. Assuming there exists an optimal coarse-graining scale at which the quality and diversity of…

A possible approach to the statistical description of granular assemblies starts from Edwards' assumption that all blocked states occupying the same volume are equally probable (S.F. Edwards, R. Oakeshott, Physica A 157, 1080 (1989)). We…

We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…

We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian…

We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics. Certain modular properties exhibited by the…

By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and…