Can the force between two magnets be described as a pure potential field?
Or is it possible to make a machine that look like a perpetum mobile, but actually takes its energy from the magnetisation of the magnets? Ie that the magnets originally have a higher energy state than after they've lost their magnetisation (should be so), and that this energy is what drives the seemingly perpetual motion.
I can think of one theoretical example where energy could be derived from a magnet's field strength, at the expense of the magnet's properties. I can't really say if it's really much of a net gain, unless you have a massive supply of free mythically-strong magnetite lying around.
Step 1: Take a bunch of magnets or magnetic material, put them on a conveyor (either a belt, pipe, or some kind of mechanical restraint) .
Step 2: Run the cargo into close proximity to a plate of material that repels it. In the easiest case, it means the magnets are sorted so that they are all oriented in opposition to a plate that is also magnetic. It can be done without sorting, just make the plate superconductive.
Step 3: Make it so the plate is attached to some kind of solenoid coil or other way of transforming kinetic energy to current or other usable form.
Once close enough, the plate will be repulsed by the cargo, pushing back against the generator, to a point.
Step 4: Heat the magnetic material until it reaches its Curie point, wherepon it will lose its magetism and the plate will push back, completing a down cycle.
Repeat with more magnets and probably lose more energy than you put in.
The problem with the non-superconductive version, besides the difficulty in sorting, is that additional energy is expended pushing the magnets into the plate's field.
The plate could be an electromagnet, but that is also a drain on the energy supplied.
The superconductive variant would avoid the issue by not cooling the plate until after the magnets are in position. Unfortunately, coolant needs energy to be generated, and the heating of the magnets would require some nifty shielding to keep the plate from warming too much. The plate would also be rather brittle and subject to a lot of mechanical stress.
In essence, this is a very low intensity version of what goes on in any other fuel-burning process. The breaking of electromagnetic bonds in a combustion engine is pretty much the same thing, only more practical.
In an inverse process, metal can be heated and then subjected to a strong magnetic field as it cools. This takes an amount of energy that can be measured to give a maximum ceiling to the energy derived. Compared to actual chemical bonds, it's not in the same league or league of leagues.
It might be useful if you need a turbine or piston drive on a world covered with liquid helium and filled with nobium magnets. Other than that, it would be a neat science project.
edit:
For those that are curious, the reason why this is so similar to coal or other chemical fuels is that magnets have a similar, coarser, version of bonding in place. The small crystals in the magnet's structure are bound physically in place. When magnetized, they are oriented in a manner where their poles are pushing against one another.
If given just a little kick, the crystals would be able to move into an arrangement where they aren't pushing against one another.
For coal, it's oxygen and a spark that lead to much less constrained waste gases. For the magnet, sufficient heat or even a lot of vibration can do the trick. However, coal is made of trillions upon trillions of such repelling atoms. A magnet's crystals are the main unit of energy storage, and they are billions of times less compact.