The Mori–Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics
The Mori–Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics
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DOI：
10.4310/cms.2019.v17.n2.a10
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发表时间：
2017-08
影响因子：
1
通讯作者：
Weiqi Chu;Xiantao Li
中科院分区：
文献类型：
--
作者：
Weiqi Chu;Xiantao Li
能量输运方程是直接从完整的分子动力学模型作为粗粒度的描述。选择局部能量作为粗粒度变量，我们应用Mori-Zwanzig形式主义导出一个简化模型，其形式为广义Langevin方程。然后引入马尔可夫嵌入技术来消除历史依赖性。与传统的能量输运模型形成鲜明对比的是，这种推导产生了空间平均能量的随机动力学模型。讨论了加性噪声和乘性噪声对随机力的近似，以保证解的统计性质。
Energy transport equations are derived directly from full molecular dynamics models as coarse-grained description. With the local energy chosen as the coarse-grained variables, we apply the Mori-Zwanzig formalism to derive a reduced model, in the form of a generalized Langevin equation. A Markovian embedding technique is then introduced to eliminate the history dependence. In sharp contrast to conventional energy transport models, this derivation yields {\it stochastic} dynamics models for the spatially averaged energy. We discuss the approximation of the random force using both additive and multiplicative noises, to ensure the correct statistics of the solution.