The quasicontinuum (QC) method was originally introduced to bridge across length scales by coarse-graining an atomistic ensemble to significantly larger continuum scales at zero temperature, thus overcoming the crucial length-scale limitation of classical atomic-scale simulation techniques while solely relying on atomic-scale input (in the form of interatomic potentials). An associated challenge lies in bridging across time scales to overcome the time-scale limitations of atomistics at finite temperature. To address the biggest challenge, bridging across both length and time scales, only a few techniques exist, and most of those are limited to conditions of constant temperature. Here, we present a new general strategy for the space–time coarsening of an atomistic ensemble, which introduces thermomechanical coupling. Specifically, we evolve the statistics of an atomistic ensemble in phase space over time by applying the Liouville equation to an approximation of the ensemble’s probability distribution (which further admits a variational formulation). To this end, we approximate a crystalline solid as a lattice of lumped correlated Gaussian phase packets occupying atomic lattice sites, and we investigate the resulting quasistatics and dynamics of the system. By definition, phase packets account for the dynamics of crystalline lattices at finite temperature through the statistical variances of atomic momenta and positions. We show that momentum–space correlation allows for an exchange between potential and kinetic contributions to the crystal’s Hamiltonian. Consequently, local adiabatic heating due to atomic site motion is captured. Moreover, in the quasistatic limit, the governing equations reduce to the minimization of thermodynamic potentials (similar to maximum-entropy formulation previously introduced for finite-temperature QC), and they yield the local equation of state, which we derive for isothermal, isobaric, and isentropic conditions. Since our formulation without interatomic correlations precludes irreversible heat transport, we demonstrate its combination with thermal transport models to describe realistic atomic-level processes, and we discuss opportunities for capturing atomic-level thermal transport by including interatomic correlations in the Gaussian phase packet formulation. Overall, our Gaussian phase packet approach offers a promising avenue for finite-temperature non-equilibrium quasicontinuum techniques, which may be combined with thermal transport models and extended to other approximations of the probability distribution as well as to exploit the variational structure.

准连续谱（QC）方法最初是通过在零温度下将原子集合整体粗粒度化为明显更大的连续谱来跨过长度标度的，从而克服了经典原子标度模拟技术的关键长度标度限制，而仅依赖于原子尺度输入（以原子间电势的形式）。一个相关的挑战在于跨时标桥接以克服原子学在有限温度下的时标限制。为了应对最大的挑战，跨越时标和时标，只有少数几种技术存在，其中大多数仅限于恒温条件。在这里，我们提出了一种用于时空粗化的新通用策略原子团的概念，引入了热机械耦合。具体来说，我们通过将Liouville方程应用于整体的概率分布的近似值（进一步允许采用变分形式）来演化随时间变化的原子态整体的统计量。为此，我们将晶体固体近似为占据原子晶格位的集总相关高斯相数据包的晶格，并研究所得的准静态和系统动力学。根据定义，相位包通过原子动量和位置的统计变化来说明有限温度下晶格的动力学。我们表明，动量-空间相关性允许对晶体的哈密顿量的势能和动力学贡献之间的交换。最后，捕获由于原子位点运动引起的局部绝热加热。此外，在准静态极限中，控制方程式简化为热力学势能的最小化（类似于先前为有限温度QC引入的最大熵公式），并且它们产生了局部状态方程式，该方程式是我们为等温，等压，和等熵条件。由于我们的无原子间相关性的配方排除了不可逆的热传输，因此我们展示了其与热传输模型的结合以描述现实的原子级过程，并且我们讨论了通过在高斯相数据包配方中包括原子间相关性来捕获原子级热传输的机会。全面的，