An analogy is that of stirring a vat of alphabet soup and noticing that there is a fair number of single-letter words popping into view ("A", "I"), a smaller number of two-letter words, an even smaller number of three-letter words ... a very very small chance of a twenty-letter word ... and a vanishingly small chance of the 189819-letter monster <https://en.wiktionary.org/wiki/Appendix:Protologisms/Long_wo...> popping into view. The stirring doesn't stop just because a multiletter word appears, so multiletter words are quickly broken up and even valid single-letter words get hidden behind the "B"s and "Q"s and other letters in the soup.
Boltzmann brains will fluctuate out of existence on the order of a small multiple of the light-crossing time of the brain-matter that fluctuated into existence. As the brains are human, they won't even have a chance to react. Although their false memories are encoded however true memories exist in our own brains, they'll have no time to have a reminiscence or notice their lack of sensory organs. (Which is probably good, since they would quickly suffer and die from lack of pressure and oxygen).
A Boltzmann-brain with a full encoding of a life worth of false memories (from never-existing sensory input) is a much larger number of letters. Also, in a cold universe, the stirring is slower, and the letters sparser. Boltzmann brains are tremendously unlikely except in a verrrrrrrrry big volume of spacetime. But with a sufficiently big volume of spacetime, or one with an energetic false vacuum, one should expect a lot of Boltzmann brains. This view puts some limits on our own cosmos's vacuum, since we don't see lots of Boltzmann brains (or even much less complicated but RADAR-detectable and/or eclipsing strucures) fluctuating into brief existence in our solar system.
Boltzmann brains are low-entropy. A persisting Boltzmann brain (fluctuating into existence and staying in existence for a long time) is much lower entropy still. This poses problems for hypotheses that the entire early universe fluctuated into existence and then evolved into the structures we see now. Here there are human brains attached to sensory apparatus, whose memories correlate fairly well with their history of input (and recordings by ancestors, and fossil records, and so on): a system with much much lower entropy than Boltzmann brains, so what suppresses relatively high-entropy structures (including Boltzmann brains) from dominating (by count) our neighbourhood?
Also, if the universe supports large low-entropy fluctuations, galaxies that briefly (~ hundred thousand years) fluctuated in and out of existence should be much more common than galaxies with a history consistent with billions of years of galactic evolution, and you'd expect random variations in morphology, chemistry, and so forth; that's not what we see.
This is a bit annoying, as it would be handy to point to Boltzmannian fluctuation theory as the source of the tremendously low entropy in the very early universe, i.e., it could have arisen spontaneously in a less precisely ordered space. Oh well.
> why would ... a universe appear to evolve from a low entropy past following a small set of laws
Thermodynamics.
The issue is: where did the low entropy past come from? Once you have that, evolving into a higher entropy structure-filled present is not too hard -- that's essentially what we have with the standard cosmology from about the electroweak epoch onwards.
So in summary:
> sequences of Boltzman brains who all subjectively experience time as sequential
whatever these might be, they aren't Boltzmann brains, since the latter don't subjectively experience anything as objectively they fluctuate out of existence in something like a nanosecond.
Very briefly, the short existence is driven by interacting fields and the need to keep entropy (relatively) high: if your starting point just before the appearance of the brain is a region that is high quality vacuum, you have to come up with protons, calcium nuclei, ... and all that requires very careful aim to have one split-second "movie frame" of brain. You need much better "aim" which really drives down the entropy (which corresponds a much larger fluctuation) to go from vacuum to a Boltzmann brain that doesn't disintegrate starting in the very next frame thanks to overshoots of momentum.
The higher the entropy of the Boltzmann brain, the clearer the stat mech argument. (If one gets stuck thinking about human brains, C. elegans apparently develop memories and store them in their nerve ring. Why isn't the outer space of our solar system full of those Boltzmann-C.-elegans brains fluctuating in and out of existence with each possessing false memories of sensory stimuli? Smaller fluctuations, so there should be many more of those than human Boltzmann brains).