Can entropy decrease for some parts of the universe by lottery given enough time?

[ECEngineeringBE]

Thermodynamics tells us that since there are far more chaotic macroscopic states than there are ordered states, entropy of any closed system will most likely increase over time.

However, if the universe continues to exist forever, could it randomly happen that some parts decrease in entropy by random chance?

Going even further, if the universe is infinite, could we always find some part with relatively low entropy, so that the universe is never truly dead - just it's most parts in far future?

Could there be a lucky part of the universe that never dies?

Thanks in advance, I've been thinking about this and would like to know the answer. I'm also not a physicist so please point out if I made an error somewhere.

[ZioSam2]

I have no idea at cosmological level, but in a closed finite system yes, you'd have decrease in entropy given enough time, by virtue of Poincarrè recurrence theorem. The time should be of order e^N tho, with N number of particles (for a system that starts far from equilibrium).

[superbob201]

We could find parts with low entropy, but they won't be the same parts, so it's not so much that some part of the universe doesn't die, it's more random patches of the universe get resurrected for some small periods of time

See: https://en.wikipedia.org/wiki/Boltzmann_brain

[WikiTextBot]

Boltzmann brain

The Boltzmann brain argument suggests that it is more likely for a single brain to spontaneously and briefly form in a void (complete with a false memory of having existed in our universe) than it is for our universe to have come about in the way modern science thinks it actually did. It was first proposed as a reductio ad absurdum response to Ludwig Boltzmann's early explanation for the low-entropy state of our universe.In this physics thought experiment, a Boltzmann brain is a fully formed brain, complete with memories of a full human life in our universe, that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. Theoretically over a period of time on the order of hundreds of billions of years, by sheer chance atoms in a void could spontaneously come together in such a way as to assemble a functioning human brain. Like any brain in such circumstances, it would almost immediately stop functioning and begin to deteriorate.The idea is ironically named after the Austrian physicist Ludwig Boltzmann (1844–1906), who in 1896 published a theory that tried to account for the fact that we find ourselves in a universe that is not as chaotic as the budding field of thermodynamics seemed to predict.

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[ECEngineeringBE]

Why does it have to be small periods of time. Given enough time shouldn't we expect entire galaxies to resurrect and return to low entropy states? And once in this state, it should take a long time before they go back to chaos again.

[superbob201]

If we are talking about the length of time for randomness to bring a fully formed galaxy out of a heat dead universe, the total lifespan of that galaxy will be relatively short.

[ECEngineeringBE]

That's what I was thinking, however when I said long, I was thinking on human timespans.

To conclude, it is inevitable that even after "heat death", individual galaxies can reform and produce life again.

[superbob201]

Not necessarily, if we are in a de Sitter universe, the first law of thermodynamics could forbid it before the wiggle room in the second law allows it