Green-Kubo relations are a fancy way of figuring out how fast particles are moving in a material. Imagine you're playing with a bunch of toy cars in a sandbox. If you wanted to know how fast all the cars were moving, you could use a special tool called a speedometer. Green-Kubo relations work pretty much the same way, but instead of a speedometer, we use a mathematical formula that takes into account the movement of atoms and molecules in a material.
When we talk about the movement of atoms and molecules, what we're really talking about is heat. Think of heat like a bunch of tiny little balls bouncing around really fast. The faster they bounce, the hotter something is. Green-Kubo relations help us figure out how fast those balls are bouncing around by looking at how much energy is being transferred between them.
So, let's say you have a block of ice on a hot summer day. The ice is cold because the molecules in the ice are moving really slowly. But when the ice starts to melt, it's because the heat from the sun is causing those molecules to move faster and faster. By using Green-Kubo relations, scientists can figure out just how fast those molecules are moving so they can better understand how materials behave under different conditions.
Overall, Green-Kubo relations are a powerful tool that scientists use to better understand how atoms and molecules move in a material. And just like how you can learn a lot about the toy cars you play with in the sandbox using a speedometer, Green-Kubo relations help scientists learn a lot about the materials they study.