According to the Maxwell's Demon paradox, we have the following conditions:

• The gasses in two boxes, connected by a door, are the same temperature.
• The devil uses the door in the middle to allow the fast (hot) molecules on the left to pass to the right.
• The devil uses the same door to allow slow molecules to pass from the left to the right.
• But we said the boxes have the same temperature for both contained gasses.
• So when the box on the right side is not completely hot, there still exists cold gas molecules in the box on the right.

However according to the thought experiment, the cold gas molecules are all collected on the left side of the chamber. Is this a contradiction in paradox? How do we explain that slow molecules move as fast as hot gas molecules?