The most efficient refrigerator is going to be the one with a material that is sticky for molecules to slow them down, but not actually sticking. No electricity required.
Well, maybe the first version would use the electricity for cleaning and non-sticking-ness, but it’ll eventually be made to use no electricity.
I’m currently not exactly sure what that “sticky” substance would be, but this would be the same thing used for “microwaves” that could also cool down food.
Another idea for cooling would first require the ability to see the molecules, position and velocity. Unfortunately, our current physics paradigm includes the Heisenberg’s Uncertainty Principle. So, we’ll need to find a way against that. Then use Newton’s Second Law (equal opposite reaction) to “zap” them, or just collide with them from the opposite direction so velocities cancel.. and less moving molecules for less temperature. This would need to fire millions (billions?) of counteracting particles, which in itself would likely cause more heat, especially for first versions. (Sdienote: Current refrigerators also produce much heat.)
Another idea for that initial “sticky” thought is that there could possibly be a mesh that had many small tunnels for molecules to pass through. The small tunnels would get smaller and smaller, and there would be a way to not have the “flow” principle of fluids speeding up through narrow bottlenecks. It would be more like things getting crowded at the tiny end of the tunnels.
Another idea would be something similar to cold welding…