The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation of particle systems as the motion of a particle in a random force field with a friction term which is due to the interaction with the surrounding particles. Some of the technical details of this method are discussed in the companion paper [50].

中文翻译：

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具有长程相互作用的相互作用粒子系统：缩放限制和动力学方程

本文的目标是描述由相互作用的粒子系统的尺度限制产生的各种动力学方程。我们提供了一种形式体系，使我们能够确定给定相互作用势和标度限制的动力学方程。我们在本文中的重点是具有长程相互作用的粒子系统。这里的推导是形式化的，但它提供了对粒子系统的解释，即粒子在随机力场中的运动，摩擦项是由于与周围粒子的相互作用而产生的。该方法的一些技术细节在配套论文 [50] 中进行了讨论。