The perpetual motion machines you refer are only that in a very metaphorical sense -- they don't allow an infinite extraction of some energy-like metric.
Glider guns produce an endless stream of gliders to give the simplest example.
Okay, so what would be your energy (or disorder) metric in that case and how does the Glider gun violate it? You need to do more than just keep overwriting zeroes with ones.
Many experts suspect that there is no polynomial-time solution to the so-called NP-complete problems, though no-one has yet been able to rigorously prove this and there remains the possibility that a polynomial-time algorithm will one day emerge. However unlikely this is, today I would like to invite LW to play a game I played with with some colleagues called what-would-you-do-with-a-polynomial-time-solution-to-3SAT? 3SAT is, of course, one of the most famous of the NP-complete problems and a solution to 3SAT would also constitute a solution to *all* the problems in NP. This includes lots of fun planning problems (e.g. travelling salesman) as well as the problem of performing exact inference in (general) Bayesian networks. What's the most fun you could have?