Non-Equilibrium Work And Dissipation in Coarse-Grained Models

如果一个人打算粗粒度的系统的动力学是热平衡，需要整合出微观状态的非稳态分布。这意味着对应于该分布的熵将随时间而变化，这反过来又意味着粗粒度变量对过程中耗散的热量有重要贡献。拟议的项目将侧重于这一问题。使用时间相关的投影算子形式主义，我们将分析在驱动系统中耗散的热量。我们将首先从理论物理的基本观点来解决这个问题，然后将我们的研究结果应用于几个数值测试案例：聚合物熔体的微观流变学，固体对固体的滑动摩擦和NaCl在水中的解离。最后，我们将发展一个考虑非定常记忆效应的分子动力学模拟尺度桥接工具。该研究单位将研究降低非平衡系统复杂性的方法。我们将应用我们的项目中开发的方法，从这个研究单位的其他几个项目的数据。

If one intends to coarse-grain the dynamics of a system that is out of thermal equilibrium, one needs to integrate out a non-stationary distribution of microstates. This implies that the entropycorresponding to this distribution will change with time, which in turn implies that there is a non-trivial contribution tothe heat dissipated during processes performed by the coarse-grained variable. The proposed project will focus onthis issue. Using a time-dependent projection operator formalism we will analyze the heat dissipated in a driven system. We will first tackle this problem from the fundamental point of view of theoretical physics and then apply our findings to several numerical test-cases: microrheology of a polymer melt, sliding friction of solids on solids and the dissociation of NaCl in water. Finally we will develop a scale-bridging tool for molecular dynamics simulation that takes non-stationary memory effects into account.This project is part of a research unit proposal. The research unit will study methods to reduce the complexity of non-equilibrium systems. We will apply the methods developed in our project to data from several other projects of this research unit.