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Question: Is it true that free energy increases don't happen naturally? Keep reading for background on what is meant by "naturally".

The idea that a decrease in entropy, even a local one, requires some kind of intelligence or life to make it happen has been around for awhile, and still pops up (for example, Local decrease in entropy, does it require life?). People produce numerous counterexamples. The counterexamples don't impress the person making the claim. "Of course I don't mean that kind of entropy decrease". The goalposts shift. The claim becomes unfalsifiable.

But intelligent design advocates have a new and improved version of the claim, which they use as an argument against naturalistic origins of life. Actually, it has apparently been around since the 1980s, but I haven't seen it addressed by anyone outside the pro-intelligent design community. And it sounds specific enough that it is either true or false.

Here's the improvement. Instead of claiming that a decrease in entropy requires intelligence, they say that an increase in free energy requires intelligence, at least through the introduction of a "machine" or "engine" to act as an energy transducer. The idea is that energy input from the surroundings without a transducer to guide it is "raw" and is therefore disruptive or destructive of order (the phrase Bull in a China Shop comes up frequently). A typical statement is found in this article from Brian Miller of the Discovery Institute, Free Energy and the Origin of Life: Natural Engines to the Rescue

In previous articles, I outlined the thermodynamic challenges to the origin of life and attempts to address them by evoking self-organizing processes. Now, I will address attempts to overcome the free-energy barriers through the use of natural engines. To summarize, a fundamental hurdle facing all origin-of-life theories is the fact that the first cell must have had a free energy far greater than its chemical precursors. And spontaneous processes always move from higher free energy to lower free energy. More specifically, the origin of life required basic chemicals to coalesce into a state of both lower entropy and higher energy, and no such transitions ever occur without outside help in any situation, even at the microscopic level.

Attempted solutions involving external energy sources fail since the input of raw energy actually increases the entropy of the system, moving it in the wrong direction. This challenge also applies to all appeals to self-replicating molecules, auto-catalytic chemical systems, and self-organization. Since all of these processes proceed spontaneously, they all move from higher to lower free energy, much like rocks rolling down a mountain. However, life resides at the top of the mountain. The only possible solutions must assume the existence of machinery that processes energy and directs it toward performing the required work to properly organize and maintain the first cell.

And a similar statement is found in Miller's article, Thermodynamics of The Origin of Life

The problem for all theories of origin of life now becomes quite evident. The simplest functional cell compared to its most basic building blocks has both lower entropy and higher energy. And, natural systems never both decrease in entropy and increase in energy at the same time. Such an event would be like rolling countless sixes in a row when the dice are strongly loaded against rolling even one. Therefore, the origin of life through purely natural processes would seem as implausible as water on a hot summer day spontaneously freezing or a river flowing unaided uphill for thousands of miles.

So, my question is whether the claim is true. Namely, that free energy never increases in "natural" systems without outside help. Or more specifically, that there is never an increase of energy and a decrease of entropy at the same time without the help of some "machines".

I can of course come up with examples where a "machine" is used to raise free energy. For example, a battery drives a chemical reaction "uphill" in an electrolytic cell. And when I asked Miller to explain this claim in the comments section of a youtube video, he simply pointed to the example of a freezer making ice on a summer day. I'm not sure where the free energy increase is involved there, but I guess the basic point is that a temperature difference is created where there wasn't one before, and that temperature difference is a source of available work. I asked him twice for more justification of the claim, but so far he's declined to give it.

Those two examples don't clearly demonstrate to me that a general principle is at work. So, is the principle true or false? Can it be proved from the Second Law of Thermodynamics? Can a counterexample be produced?

I am not asking if intelligent design/creationism is true. I am not asking if a local decrease in entropy can happen.

ether
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The most fundamental counter-argument I can think of is fairly simple. Thermodynamics by its very definition describes the behaviour of equilibrium states (typically local). The living organism is definitely out of equilibrium so you cannot make simplistic claims about entropy or free energy. It is very typical that energy and matter fluctuations lead to the formation of high-density regions in your system: stars and planets in cosmology or cells and living organisms on lower length scales. To apply the thermodynamic reasoning you have to look at the times far greater than the equilibration time (which for the earth are stupendously large). And in the (very) long-term there is no life, only the heat(entropy?) death of the universe.