Roger Penrose has really mind-bending observation and theory about the time past heat death in the 'Cycles of Time'.
After 10e100 years when there is only massless particles like photon's left and black holes have evaporated, time essentially stops existing. Photons, gluons and gravitons just go without any new events to infinity.
What you're describing is still technically Heat Death. I'm talking about after that. Technically, if anything can still evaporate, you're not yet at true Heat Death.
But infinity is a larger number than even the exceedingly unlikely probability of Entropy spontaneously reducing, just like there's a finite possibility of all the air deciding to move to the other side of the room without any external actions. Quantum fluctuations can produce stuff from nothing, they just never do with any appreciable probability.
Also listened to this and was mind-blown. But my take away was that at this point photons can then "make it to infinity" which sort of meant they will get through to (or cause?) the next big bang. Maybe all the photons combine and cause the big bang? One thing I didn't understand was that he said this meant that signals could make it through to the next iteration of the universe. However my understanding was that all photons are scattered by the surface of last scattering (CMBR), so how could this be possible?
Spontaneous entropy decrease that leads to Big Bangs at least every 10^10^10^56 years.
Well after heat death and "final" energy state of the Universe.
10^10^10^56 years sounds like a long time, but it's way smaller than infinity... Imagine Graham's number, which is still finite and thus much smaller than infinity...
https://en.wikipedia.org/wiki/Graham%27s_number
Ah, but that merely reduces their probability. Over an infinite timeline, anything with a small but still finite probability of happening will eventually happen (and, I think you could say, happen an infinite number of times...).
After 10e100 years when there is only massless particles like photon's left and black holes have evaporated, time essentially stops existing. Photons, gluons and gravitons just go without any new events to infinity.