期刊
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
卷 73, 期 -, 页码 242-268出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2014.09.008
关键词
Non-equilibrium statistical thermodynamics; Binary alloys; Meanfield theory; Variational updates; Slow kinetic processes
资金
- Department of Energy (DoE) National Nuclear Security Administration (NNSA) through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials [DE-FC52-08NA28613]
- Lawrence Livermore National Laboratory (LLNL) [B579041, DE-AC52-07NA27344]
- U. S. Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) [W911NF-11-R-0001]
- Caja Madrid foundation
- Ministerio de Economia y Competitividad of Spain [DPI2012-32508]
We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jaynes' 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. (C) 2014 Elsevier Ltd. All rights reserved.
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