> what's the 'order' which 'the biological system' is trying to maintain?

Being stable, ie. not entering a cascade of events that leads to death.

> And what's a 'free energy functional'?

"free energy functional of their internal states" means the free energy, computed as a function from their internal state. ie. each internal state has a corresponding internal energy.

> The title sounded like a perpetuum mobile, but that doesn't seem to be it.

Actually, it is. It's just a very very complex mobile. With some energy input (drinking, photosynthesis, ...) and some energy output (heat, sweat, ...)

> Can someone ELI5 what this article is about?

I'm going to try, but I'm no biologist or chemist so I can't certify this is correct.

Living beings are very complex systems, which could easily enter a bad state, which would lead to a worse state, etc until death.

To prevent that, they restrict themselves to some "good" states, which have little "free energy". The thing with "free energy" is that it cannot increase easily, so the beings cannot enter a state with higher "free energy" than they currently have.

If all possible bad states have higher "free energy" than the current state, then they cannot reach it, which is good.

>Living beings are very complex systems, which could easily enter a bad state, which would lead to a worse state, etc until death.

I'm still equally confused as OP, right at this initial building block.

A state is just a collection of atoms in a certain configuration. Some states make up a living creature. Some others make up a dead creature. Most creatures want to avoid transitioning from an alive state to a dead state. Most of the time you would say that most creatures want to avoid dying, but because of the ideas that come next it is important to start talking in terms of states.

> "free energy functional of their internal states" means the free energy, computed as a function from their internal state. ie. each internal state has a corresponding internal energy.

I think what is confusing people (it is certainly confusing me) is the distinction between a function and a functional.

Both are the same thing (kind of)

The name “functional” is commonly used to refer to a function which takes a whole function (rather than, say, a number) as input. A simple example of a functional is the definite integral (area under the curve) over an interval.

Think about an atom bomb. Large amount of energy is released in a small space. This energy is always there but we don't see huge explosions everywhere.

I think it's about https://en.wikipedia.org/wiki/Tragedy_of_the_commons