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

My understanding is that entropy refers to (edit: something proportional to the inverse of the) number of constraints on how energy is distributed, ultimately throughout the entire universe. It must always increase, but this may happen at faster/slower rates.

Constructing a building essentially amounts to taking relatively high energy (visible, UV, etc) light 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 outerspace.

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

How about if the buildings were never constructed because Earth had higher cloud cover albedo (like Venus) and reflected those photons into space instead of converting the energy into trees, oil, and waste heat?

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    $\begingroup$ Say you want to make a building out of 10 bricks and one out of 100 bricks. You must expend energy to arrange the bricks. According to the Second Law, there will be more entropy generated in doing so (in the form of heat) than is reduced in organizing the bricks. I would expect that the more bricks one must arrange, the more energy is wasted. That is to say, all things being equal, the larger process would have the larger net entropy increase. But I am no expert thermodynamicist. $\endgroup$ Jan 3, 2021 at 23:45
  • $\begingroup$ So you'd expect the contribution of waste heat to be much greater than any loss in entropy from organizing the bricks. That makes some sense. Im not even sure if making and organizing the bricks is a net loss either though. Eg, as discussed here the entropy = disorder concept is misleading: entropysite.oxy.edu It could be that the energy has more available microstates (less constraints, more entropy) when in the building than the original solar photons as well. I have no idea how to estimate that though. $\endgroup$
    – Livid
    Jan 4, 2021 at 0:03
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    $\begingroup$ The change in thermodynamic entropy from rearranging bulk objects is negligible. You'll never get close to the way that Nature rearranges $10^{10}$, $10^{20}$, $10^{30}$ molecules at a time. Of the construction materials, I'd expect the waste heat from concrete curing to predominate in terms of entropy production. $\endgroup$ Jan 4, 2021 at 0:09
  • $\begingroup$ 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 bulk objects in the final step. Trees growing to form the wood, etc. $\endgroup$
    – Livid
    Jan 4, 2021 at 0:20

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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 bulk objects in the final step. Trees growing to form the wood, etc.

All of these processes involve entropy generation. Trees etc. 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 obviously switch, constructing the skyscraper would result in a smaller entropy increase!

We can stop the answer here, but let me just make one more quick comment. As others said, rearranging blocks to make a building out of it contributes very very little to a decrease in entropy (if at all, depending on exactly how you view entropy). I think you were wondering more about making the blocks as opposed to rearranging them, but if a block has a lower entropy than the building materials that went into it, then that would just be another example of one of those subsystems whose entropy was lowered by some sort of engine with a less than 100% efficiency at the cost of increasing the entropy of everything else by a bigger amount.

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  • $\begingroup$ "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. $\endgroup$
    – Livid
    Jan 4, 2021 at 11:12
  • $\begingroup$ 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. $\endgroup$
    – Livid
    Jan 4, 2021 at 11:22
  • $\begingroup$ The short answer is yes. 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. $\endgroup$ Jan 4, 2021 at 11:28
  • $\begingroup$ 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 $\endgroup$ Jan 4, 2021 at 11:42
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    $\begingroup$ 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. $\endgroup$ Jan 4, 2021 at 11:51

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