When simulating fluids, molecule by molecule, it is way too much information to keep track of. Particles represent convenient storage quantities derived deep down from quantum mechanics. Providing a high-level perspective of the sub-atomic origin. Sacrifice the molecules to get a clearer view on overall fluid behaviour. In terms of macroscopic information, we get a cleaner view by averaging. ![[Pasted image 20220221190341.png]] #### Particles Collective Behaviour ![[Pasted image 20220221190631.png]] ![[Pasted image 20220221190651.png]] No matter how we kick off the particles, there is a microscopic mechanism at work, that smooths out the initial distortions to the speed and position. With time, there is equilibrium. Co-ordinate distributions establish. Position: There is a natural probabilistic tendency to even out the position distribution. Particles get pushed away from energetic occupied regions. Speeds: Faster particles are more likely to slow down and slower particles are more likely to speed up. ![[Pasted image 20220221191825.png]] #### Using Equilibrium for Reduction Enough molecular collisions could equilibrate the fluid locally. ![[Pasted image 20220221192408.png]] For homogenous fluid states, location and speed are well described by few characteristic quantities.