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Prerequisite

In this section, we will provide a brief overview of fundamental prerequisites before delving into the topic of Langevin. Experienced individuals in the field of physics may opt to bypass this segment. Nevertheless, it is essential to note that this section covers foundational conceptual knowledge that will be utilized in subsequent discussions.

Diffusion Equation

Einstein Relation in Diffusion Equation

Introduction of Markovian Langevin

Consider the situation of an open system exchanging energy with a heat bath. If there is a strong time scale separation between the dynamics of the heat bath and the explicitly modelled degrees of freedom, the exchange of energy between these two systems is well modelled by a Markovian process.

Open System and Modelled Degrees of Freedom

Introduction of Non-Markovian Langevin

If we consider a system consisting of a distinguished particle surrounded by collection of particles of approximately the same mass, then a reduced model where the interaction between the distinguished particle and the solvent particles is replaced by a simple Langevin equation would lead to a poor approximation of the dynamics of the distinguished particle.