Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

Newtonian Event-Chain Monte Carlo and Collision Prediction with Polyhedral Particles

Polyhedral nanocrystals are building blocks for nanostructured materials that find applications in catalysis and plasmonics. Synthesis efforts and self-assembly experiments have been assisted by computer simulations that predict phase equilibria. Most current simulations employ Monte Carlo methods, which generate stochastic dynamics. Collective and correlated configuration updates are alternatives that promise higher computational efficiency and generate trajectories with realistic dynamics. One such alternative involves event-chain updates and has recently been proposed for spherical particles. In this contribution, we develop and apply event-chain Monte Carlo for hard convex polyhedra. Our simulation makes use of an improved computational geometry algorithm XenoSweep, which predicts sweep collision in a particularly simple way. We implement Newtonian event chains in the open-source general-purpose particle simulation toolkit HOOMD-blue for serial and parallel simulation. The speedup over state-of-the-art Monte Carlo is between a factor of 10 for nearly spherical polyhedra and a factor of 2 for highly aspherical polyhedra. Finally, we validate the Newtonian event-chain algorithm by applying it to a current research problem, the multistep nucleation of two classes of hard polyhedra.

Structural and thermodynamic properties of hard-sphere fluids

This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixtures are also discussed.

Integration through transients approach to the μ(I) rheology

This work generalizes the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)10.1103/PhysRevLett.121.148002] to the determination of the pressure. We focus on the Bagnold regime and provide theoretical support to the empirical μ(I) rheology laws that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the μ(I) laws apply.

Performance of the asymptotic expansion method to derive equations of state for hard polyhedron fluids

The asymptotic expansion method is used to derive analytical expressions for the equations of state of 14 hard polyhedron fluids such as cube, octahedron, rhombic dodecahedron, etc., by knowing the values of only the first eight virial coefficients.

Predicting maximally random jammed packing density of non-spherical hard particles via analytical continuation of fluid equation of state

We developed a formalism for accurately predicting the density of MRJ packing state of a wide spectrum of congruent non-spherical hard particles in 3D via analytical fluid EOS.