Why can a messy room not clean itself? The messy room analogy is not perfect since the items in the room are not mobile like particles. There is a difference between high entropy in an immobile disorganized static (stopped) state versus high entropy in a dynamic (mobile) state.
If the clothes and other objects in the room were all moving due to brownian motion, they would be dynamic. In the above thought experiment imagine clothes,shoes, and other objects moving randomly in a room which has aluminum walls. Imagine one magnet exists in the room which also moves randomly. The clothing and shoes bash into the magnet randomly.
If the clothing and shoes start out with an initial speed, after time they will come to a full stop due to eddy dampening from eddy currents generated in the aluminum by the magnet.
This is why the messy room analogy is not a tight analogy, since a messy room is not full of mobile moving objects by themselves. Whereas in a container of particles all the objects are moving. In the case of slowing down the particles in a liquid to cool it, the scientist does not care about the final order/positions of the particles if the goal is just to slow down the particles and cool them in a lower entropy state. As long as the fluid cools and the particles end up in any order clumped closer together, the scientist is satisfied with his goal of cooling the fluid down. Whereas with a messy room one wants to put the items back in certain places (dresser, closet, etc.) and the final positions of the objects matter. If the goal was to have all the objects in the messy room clump together in one pile, and they were all initially moving, the messy room analogy would be more direct. This is why analogies can be bad. Can we cool a fluid by emulating a cold particle (causing drag) is the question to ask out of all these thought experiments. If so, then the second law is no longer true in those cases. It would be spectacular if the second law were falsified using nano technology, as then global warming could be solved.