Build a skyscraper, reduce entropy?

Sometimes we are told that entropy is a measure of disorder, and disorder in the Universe always increases. So in which case does this disorder increase more: if we make a large ordered structure, like a skyscraper, or a smaller one, like a small house?

This is essentially what this question from the Stack Exchange was trying to explore. Once we resolved it, an interesting idea came up: 

If we know which process creates more disorder, can we use this to predict the future? 

Q. I'm trying to understand how entropy relates to the generation of complex systems.

Constructing a building essentially amounts to taking relatively high energy from the sun, using it to arrange various materials in a certain way (including plants creating wood, mining metals, burning fuel, etc), and eventually emitting a greater number of lower energy photons ("waste heat") into outer space.

So does building a (relatively complex) skyscraper result in greater entropy production from sunlight than a (relatively simple) single person house?

I'm asking about the total change in entropy from the original solar photons to the final building. Far more goes into that than rearranging building blocks in the final step. Trees growing to form the wood, etc.

A. All of these processes involve entropy generation. Trees and other living things are basically a collection of mini-engines that process low entropy fuel (photons, food) into generating useful energy, fixing themselves, growing, and emit waste products like any engine.

All of the above-mentioned jobs living things do can be described like this: the living thing is trying to lower the entropy of some subsystem (basically itself plus the building blocks from which it grows), at the cost of increasing the entropy of everything else.

Of course, all of these processes are not even close to 100% efficient, so all of them result in a net entropy increase. At an even more basic level, we can just say that all of these processes are off-equilibrium, irreversible processes, which again means a net entropy increase.

OK, so which results in a greater net entropy increase, a skyscraper or a small building? You can just view building a skyscraper as essentially first making a small building, and then adding many more stories on top of it. 

More irreversible processes (powering our machinery, using our muscles etc.) to convert natural stuff into stuff we want means more entropy generation.

We should be careful here about what we are actually comparing though. If the comparison was, say, between:

(a) using a bunch of low entropy photons from the sun to generate energy and everything else we need to build the skyscraper, and

(b) letting all of those same photons to just fall on the ground and heat it up, instead of being caught by plants or something else that wouldn't waste them and would use them to lower the entropy of some subsystem,

then the answer would switch, constructing the skyscraper would result in a smaller entropy increase!

Q. "All of these processes involve entropy generation." Every process must yield net entropy generation right? It is just a matter of how much. Local entropy may decrease but my understanding is that overall nothing happens in the universe unless total entropy is increased. What Im trying to understand is if this is a "force" driving the generation of ever more complex phenomena, since higher complexity seems to entail greater entropy generation. And ultimately on earth this amounts to turning relatively few high energy solar photons into many more lower energy IR photons. 

A. The "force" driving the generation of ever more complex phenomena is the low entropy condition of the Universe at the Big Bang, and its continual winding down towards the heat death. That's what allows complex structures such as life to emerge, continue to function, and for some living things to build other complex structures such as skyscrapers. 

Q. Then could we say building a skyscraper (and all the supply lines, society, etc required for that) is thermodynamically favored over building a simpler house? Ie, at a minimum more waste heat is generated in the process. 

A. I wouldn't use the term "thermodynamically favored" in this case. That term implies that one outcome is more likely than the other. But we can't predict that a skyscraper is more likely to be built than a regular building from the fact that the former will create a bigger increase in entropy. Why not? For the same reason that we can't predict that our sun will have completely burned out by tomorrow. The sun being completely burned out tomorrow is the higher entropy state compared to it being only very slightly more burned out than it is today, but we obviously wouldn't say that it's therefore more likely to happen. All we can say about the sun is that tomorrow it, along with all the radiation it generates, will have a higher entropy than today. And the same thing for our planet. Maybe somebody will build a small building, or maybe a large one, or maybe some useful energy will just get wasted. 

Q. Thanks, does that also mean generating entropy faster is then favored over slower though? Thus nature "selects" for phenomena that can allow more entropy production over those that can't. For the earth, I'm thinking that would mean anything that accelerates its progression towards becoming a zero albedo blackbody in thermal equilibrium with the sun is favored. 

A. No, generating entropy faster is not favored over slower. That was what I was trying to express with my example of the sun. Thermodynamics doesn't tell us much about the rate at which the second law works. 

Q. I see thanks. Seems like there could be something about relaxing constraints on energy flow (via complexity) accelerating entropy production going on though. Eg, uranium concentrated by humans into a nuclear reactor will decay faster than distributed in the earth. Then that allows easier creation of more nuclear reactors, spacecraft distributing mass (energy) across the solar system in ways that otherwise couldnt happen, etc. But perhaps there is no simple law there. 

A. "But perhaps there is no simple law there." Amen to that!