I am reading a paper* about the application of the maximum entropy production (MEP) in Earth science (I'm new to MEP btw). The authors start with the system of gas molecules first. When the system is isolated, it has the maximum entropy and the molecules are distributed randomly. When it get contacted with the hot reservoir, nearby molecules will have higher energy, therefore moving faster and will tend to move to the other side, while colder molecules are not really active, so they will stay in their positions. As a consequence. the molecules will shift to the cold side.
When we replace the hot reservoir with the equator, and the cold reservoir with the pole, we will have the model of planetary system.
However, doesn't that mean that more matter will locate in the pole(s) than the equator? In Earth, this would mean that there will be more structured or ordered matters, including organisms in the poles than the equator. This doesn't look right to what we know.
How can this be explained?