Not sure what you mean by the entropy change comment.
Steel has a fatigue limit, at stresses below this the steel will not grow fatigue cracks regardless of how many times the stress is applied. I haven't read the wikipedia article below (can't be bothered!) but I dare say it will go into this in some detail.
http://en.wikipedia.org/wiki/Metal_fatigue
So if a bike frame is designed from steel with sufficient tube thickness and diameter to ensure that this fatigue limit is never reached then theoretically the bike will last forever! Of course it is not that simple as fatigue is not the only failure mechanism. Corrosion and corrosion-fatigue would both affect steel frames and the method of construction and design can result in the frame being locally stressed to start with.
Equally an aluminium frame can be designed such that the stresses is sees result in a such a long fatigue life that it will effectively 'never' fail by fatigue. But to do this they need thicker and oversized tubes than for steel. Aluminium alloys are also much less strong than steel alloys used for constructing bikes. So, for the same strength frame they need more material.
So even though aluminium alloys are much less dense than steel, the resulting frames are often similar weights. The aluminium frames will tend to have larger diameters and thicker sections, resulting in a stiffer bike. Hence the stereotype of a harsh ride on aluminium and a whippy 531c frame.
The upshot of all this is that good bike frames can be made out of lots of materials. No bikes last for ever and light frames are unlikely to have the longevity of a more heavyweght design, regardless of the material it is constructed from.