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The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The…
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…
The concept of jamming has attracted great research interest due to its broad relevance in soft matter such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to the sphere packing problem and optimization…
There are a finite number of distinct mechanically stable (MS) packings in model granular systems composed of frictionless spherical grains. For typical packing-generation protocols employed in experimental and numerical studies, the…
Volume calculation of configurational spaces acts as a vital part in configurational entropy calculation, which contributes towards calculating free energy landscape for molecular systems. In this article, we present our sampling-based…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square well potential,…
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 compute the low-temperature configurational entropy of a two-dimensional supercooled liquid. Our method, based on a higher-dimensional version of the Grassberger--Procaccia algorithm, can be implemented in a manner that is entirely…
This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks…
Unraveling the complexities of random packing in three dimensions has long puzzled physicists. While both experiments and simulations consistently show a maximum density of 64 percent for tightly packed random spheres, we still lack an…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
The repulsive term of Van der Waals equation of state has been deduced and improved in this work using a probabilistic description of the configurational entropy. The aim is to find out whether its physical basis is suitable for the study…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
The entanglement properties of systems in which elastic and inelastic reactions occur in projectile-target interactions is studied. A new measure of entanglement, the scattering entropy, based on the unitarity of the $S-$matrix (probability…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Isotropic pairwise interactions that promote the self assembly of complex particle morphologies have been discovered by inverse design strategies derived from the molecular coarse-graining literature. While such approaches provide an avenue…
We propose a computational method to measure the configurational entropy in generic polydisperse glass-formers. In particular, our method resolves issues related to the diverging mixing entropy term due to a continuous polydispersity. The…
The application of concepts from equilibrium statistical mechanics to out-of-equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. For dissipative jammed systems-- particulate…
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics…