The influence of the environment on the dynamics of a sub-system has two components: a random force that the environment exerts on the small system and a friction force, a feedback that describes the response of the environment to the dynamics of the sub-system. In general, this response of the environment is retarded, the environment keeping a memory of the past dynamics of the sub-system. The contraction of information that occurs when only the dynamics of the sub-system is considered was formalized by Mori and Zwanzig, who introduced the formalism of projection operators to single out the relevant degrees of freedom. This approach provides not only the generalized Langevin equation governing their evolution, but also an explicit expression for the memory kernel describing the retarded force. I will discuss recent algorithms introduced to computed projected correlation functions from Molecular Dynamics simulations, including the memory kernel [1]. I will show how this allow to investigate the properties of the « noise » and friction kernel. I will illustrate these ideas by considering diffusion in a simple Lennard-Jones fluid and of ions confined in clays [2].

 

[1] Two algorithms to compute projected correlation functions in molecular dynamics simulations. Antoine Carof, Rodolphe Vuilleumier, and Benjamin Rotenberg. The Journal of Chemical Physics 140, 124103 (2014); doi: 10.1063/1.4868653

 

[2] Coarse graining the dynamics of nano-confined solutes: the case of ions in clays. Antoine Carof, Virginie Marry, Mathieu Salanne, Jean-Pierre Hansen, Pierre Turq & Benjamin Rotenberg (2014) Molecular Simulation, 40:1-3, 237-244, DOI: 10.1080/08927022.2013.840894