Atomistic long-term simulation of heat and mass transport
We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jayne's maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman-Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomic-level properties while simultaneously entailing time scales much longer than those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable.
© 2014 Elsevier Ltd. Received date: 1 February 2014; revised date: 29 May 2014; accepted date: 18 September 2014; Available online 30 September 2014. G.V. and M.O. gratefully acknowledge the support of the Department of Energy (DoE) National Nuclear Security Administration (NNSA) under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials as well as the support from the Lawrence Livermore National Laboratory (LLNL) through Sponsor Award No. B579041 from Prime Contract No. DE-AC52-07NA27344. M.O. and K.W. gratefully acknowledge support from the U. S. Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under Award Number W911NF-11-R-0001. Support from the Caja Madrid foundation for the sabbatical stay of I.R. at Caltech is gratefully acknowledged. P.A. gratefully acknowledges the support of the Ministerio de Economía y Competitividad of Spain (DPI2012-32508).