Let's ask ourselves this question –will our knowledge about a system increase or decrease when the system cools down?

When it's hot, there is high uncertainty about position and speed of the molecules composing the system. The more temperature goes down, the more precise your knowledge about position and speed will be.

Because von Neumann says that entropy is the missing information between a macroscopic description and a microscopic one, you have the answer –entropy goes down when temperature goes down. At 0 kelvin, the macroscopic description gives you exactly the same information than the microscopic one, therefore the entropy is zero....