You can write a program general enough to be a universe but which doesn't involve temperature and doesn't involve inevitable information loss over time. Obviously none of them are going to be generating information from nowhere, but in principle it's at least possible to break even. (One example, which is rather simple and almost borders on cheating, would be to include an API that would allow any agent to access any bit of information from any point in the past. As far as I can tell, there's no reason why this wouldn't be allowed. It would have the aesthetic disadvantage of having a fundamentally directional time dimension, but that shouldn't cause any real problems to any agents living within it.)
doesn't involve inevitable information loss over time.
Actually the lack of loss of information over time is precisely what generates the 2nd law of thermodynamics. Specifically, since all information from the past must thus be stored somewhere (unfortunately often in a way that's hard to access, e.g., the "random" motion of atoms) that continuously leaves less room for new information.
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?