Nonequilibrium thermomechanics of Gaussian phase packet crystals: application to the quasistatic quasicontinuum method

The quasicontinuum method was originally introduced to bridge across length scales -- from atomistics to significantly larger continuum scales -- thus overcoming a key 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. 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 strategy for the space-time coarsening of an atomistic ensemble, which introduces thermomechanical coupling. We investigate the quasistatics and dynamics of a crystalline solid described as a lattice of lumped correlated Gaussian phase packets occupying atomic lattice sites. 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, within the quasistatic approximation the governing equations reduce to the minimization of thermodynamic potentials such as Helmholtz free energy (depending on the fixed variables), and they yield the local equation of state. We further discuss opportunities for describing atomic-level thermal transport using the correlated Gaussian phase packet formulation and the importance of interatomic correlations. Such a formulation offers a promising avenue for a finite-temperature non-equilibrium quasicontinuum method that may be combined with thermal transport models.