扩散分子动力学的理论探讨
A Theoretical Examination of Diffusive Molecular Dynamics
AI总结：
本文提出基于相对熵的数学框架，用于研究扩散分子动力学算法，重点在于通过熵项改进空位扩散模型。
摘要：
扩散分子动力学是一种新的材料模型，具有原子级分辨率，能够达到扩散时间尺度。该方法的主要思想是首先最小化系统的近似变分高斯自由能，相对于平均原子坐标（在许多振动周期内进行平均），然后进行扩散步骤，其中原子和空位（或二元合金中的两种物种）通过主方程在扩散时间尺度上流动。我们提出基于相对熵，或Kullback-Leibler散度的数学框架，用于研究该算法。这为算法的实现和解释提供了更大的灵活性。我们然后将依赖于相对熵和测度绝对连续性的 formulations 与现有 formulations 进行比较。方程之间的主要差异出现在空位扩散模型中，其中我们的开发中出现了额外的熵项。
英文摘要：
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy of the system with respect to the mean atomic coordinates (averaging over many vibrational periods), and to then to perform a diffusive step where atoms and vacancies (or two species in a binary alloy) flow on a diffusive time scale via a master equation. We present a mathematical framework for studying this algorithm based upon relative entropy, or Kullback-Leibler divergence. This adds flexibility in how the algorithm is implemented and interpreted. We then compare our formulation, relying on relative entropy and absolute continuity of measures, to existing formulations. The main difference amongst the equations appears in a model for vacancy diffusion, where additional entropic terms appear in our development.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
