Good point -- I've struggled with the same problem, in different terms. Let me know if my statement of the problem matches the point you're making here:
"It's possible to discover, not just particulars about individual systems, but universal laws. These universal laws put a constraint on all future observations, thus reducing the subjective entropy of the universe, without (apparently) needing any corresponding gain of entropy."
It's something I was wondering about when going over the E. T. Jaynes papers and Yudkowsky's Engines of Cognition.
I haven't gotten it resolved in terms of 2nd law and the "subjective entropy" idea, but I think I know how to resolve it in the context of the simulated universe question: basically, if the simulation starts out adhering to the invariances that have to be obeyed (even though they might be more than necessary to fool observers), then it is no additional burden for the observers to notice these invariances.
Though the observers have (apparently) violated the 2nd law -- and this is an area for further research -- the simulator was already expending the computational resources necessary to make the invariances hold. It is an exception to the general principle I derived, in that it's a case where net destruction of entropy requires no additional RAM.
I'm still working on how to resolve the remaining problems, but it shows how discovery of universal physical laws needn't be a problem for the simulator.
I'll try to bring your solution back to thermodynamics terms:
The universe always has and always will obey certain invariances, and those are a redundancy in your observations, which (along with any other redundancy that could possibly be derived) is already taken into account when computing information-theoretic entropy. If you had plenty of data already to derive the invariance but just hadn't previously noticed it, that lack of logical omniscience is why the 2nd law is an inequality. Including the invariance into your future predictions isn't a net reduc...
Parapsychologists are constantly protesting that they are playing by all the standard scientific rules, and yet their results are being ignored - that they are unfairly being held to higher standards than everyone else. I'm willing to believe that. It just means that the standard statistical methods of science are so weak and flawed as to permit a field of study to sustain itself in the complete absence of any subject matter.
— Eliezer Yudkowsky, Frequentist Statistics are Frequently Subjective
Imagine if, way back at the start of the scientific enterprise, someone had said, "What we really need is a control group for science - people who will behave exactly like scientists, doing experiments, publishing journals, and so on, but whose field of study is completely empty: one in which the null hypothesis is always true.
"That way, we'll be able to gauge the effect of publication bias, experimental error, misuse of statistics, data fraud, and so on, which will help us understand how serious such problems are in the real scientific literature."
Isn't that a great idea?
By an accident of historical chance, we actually have exactly such a control group, namely parapsychologists: people who study extra-sensory perception, telepathy, precognition, and so on.
There's no particular reason to think parapsychologists are doing anything other than what scientists would do; their experiments are similar to those of scientists, they use statistics in similar ways, and there's no reason to think they falsify data any more than any other group. Yet despite the fact that their null hypotheses are always true, parapsychologists get positive results.
This is disturbing, and must lead us to wonder how many positive results in real science are actually wrong.
The point of all this is not to mock parapsychology for the sake of it, but rather to emphasise that parapsychology is useful as a control group for science. Scientists should aim to improve their procedures to the point where, if the control group used these same procedures, they would get an acceptably low level of positive results. That this is not yet the case indicates the need for more stringent scientific procedures.
Acknowledgements
The idea for this mini-essay and many of its actual points were suggested by (or stolen from) Eliezer Yudkowsky's Frequentist Statistics are Frequently Subjective, though the idea might have originated with Michael Vassar.
This was originally published at a different location on the web, but was moved here for bandwidth reasons at Eliezer's suggestion.
Comments / criticisms
A discussion on Hacker News contained one very astute criticism: that some things which may once have been considered part of parapsychology actually turned out to be real, though with perfectly sensible, physical causes. Still, I think this is unlikely for the more exotic subjects like telepathy, precognition, et cetera.