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MTW has a cute argument on p. 980 that the maximum power radiated from any system is a fixed number, about 10^53 W. I came across this and filed it away as a piece of cool trivia. But it turns out that apparently you can derive the GR field equations from nothing more than the assumption that there is a maximum power across any surface:
Jacobson, "Thermodynamics of spacetime: the Einstein equation of state," PRL 75 (1995) 1260, http://arxiv.org/abs/gr-qc/9504004
C. Schiller has made an attempt to present this at a lower mathematical level in Motion Mountain, v. II, ch. 4: http://motionmountain.net/
Schiller's treatment, unforunately, seems to veer wildly between different levels of sophistication, and I wasn't able to make much of it.
Jacobson, "Thermodynamics of spacetime: the Einstein equation of state," PRL 75 (1995) 1260, http://arxiv.org/abs/gr-qc/9504004
C. Schiller has made an attempt to present this at a lower mathematical level in Motion Mountain, v. II, ch. 4: http://motionmountain.net/
Schiller's treatment, unforunately, seems to veer wildly between different levels of sophistication, and I wasn't able to make much of it.