电荷调控系统中的电荷涨落：对统计系综的依赖性

Fluctuations in Shear-Jammed States: A Statistical Ensemble Approach

Granular matter exists out of thermal equilibrium, i.e. it is athermal. While conventional equilibrium statistical mechanics is not useful for characterizing granular materials, the idea of constructing a statistical ensemble analogous to its equilibrium counterpart to describe static granular matter was proposed by Edwards and Oakshott more than two decades ago. Recent years have seen several implementations of this idea. One of these is the stress ensemble, which is based on properties of the force moment tensor, and applies to frictional and frictionless grains. We demonstrate the full util…

Stress-stress fluctuation formula for elastic constants in the NPT ensemble

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the $NPT$ ensemble based on known expressions in the $NVT$ ensemble. We validate the formula in the $NPT$ ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by compari…

各向异性带电球体间电荷调控静电相互作用的闭式理论

A closed-form theory of charge-regulated electrostatic interactions between anisotropically charged spheres

本研究提出融合电荷调控与斑状特性的闭式理论，推导各向异性带电球体的相互作用能，应用于两种蛋白质时可复现实验数据并预测吸引态条件的扩展。

Fluctuations in the Ensemble of Reaction Pathways

The dominant reaction pathway (DRP) is a rigorous framework to microscopically compute the most probable trajectories, in non-equilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about the reaction mechanism and can be used to estimate non-equilibrium averages of arbitrary observables. On the other hand, at sufficiently high temperatures, the stochastic fluctuations around the dominant paths become important and have to be taken into account. In this work, we develop a technique to systematically include the effects of such stochastic fluctuatio…

General Theory of Statistical Fluctuations with Applications to Metastable states, Nernst Points, and Compressible Multi-component Mixtures

The general fluctuation theory is reviewed with special attention to the role played by different ensembles, and is extended to incorporate stationary metastable states obtained in the long time limit. The fluctuation in a quantity depends on the nature of the ensemble and contains at most n different fluctuation contributions, where is the number of fluctuating extensive quantities in the ensemble. We prove four general theorems and a corollary for statistical fluctuations valid for any thermodynamic system. We also demonstrate by two examples that the results of the theory remain valid regar…

Charge regulation in ionic solutions: thermal fluctuations and Kirkwood-Schumaker interaction

We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a mono-valent salt solution, considering cases where the net charge can either change sign or remain of the same sign depending on these local parameters. The charge regulation, in both cases, is described with the proper free energy function for each of the macroions, while the coupling between the charges is evaluated on the approximate Debye-Hückel level. The charge correlation functions and the ensuing charge fluctuation forces are calculat…