Could heat death be avoided in cosmology? I found this old article by Steven Frautschi 1 which talks about avoiding heat death by a hypothetical advanced civilization able to group Black Holes in clusters. He writes that in this way, the civilization could endure forever by consuming the energy from the Black Hole (for example, taking the emitted Hawking radiation)
However, wouldn't there be an end to this source? Wouldn't all black holes evaporate evetually, leaving the civilization with no energy sources left?
And if this mechanism would not work, could anything avoid heat death somehow? Perhaps, the expansion of the universe itself could avoid it in some way?
 A: The paper assumes $Λ=0$ and $k\le 0$, in which case there is no cosmological horizon and you have access to arbitrarily large amounts of matter over arbitrarily large time scales. The idea is that the universe doesn't end up in the highest entropy state because clumping doesn't naturally occur above a certain scale, so you can do work indefinitely by actively gathering and clumping matter on larger and larger scales. I suppose that eventually you will stop finding black holes at the frontier, because the largest naturally occurring ones will have evaporated, but I don't think it matters, because evaporation doesn't change the energy density. In fact, a gas of elementary particles is better because it's a lower entropy state than the black holes would have been.
He points out at the very end that this scheme won't work because there is not enough energy available to repair damage caused by quantum noise (tunneling), but that doesn't necessarily rule out some other workable approach existing in these cosmologies.
If $Λ>0$ then the whole idea is hopeless, because on every causal patch there is a finite maximum entropy (the Bekenstein entropy of the cosmological horizon, roughly $1/Λ$ in Planck units), and an actual heat death takes place.
A: Heat death (thermal equilibrium) is (and/or "has been")
avoided in at least two cosmological models, resulting (to whatever extent those models are correct) in past- and future-eternality.
One of them, described at https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology, was formulated in 2010 by Sir Roger Penrose, knighted for his achievements in mathematics and physics, and awarded a 2020 Nobel Prize in Physics for some of his work on black holes.
In his model, all astronomical objects are eventually (over a phenomenally long timespan) absorbed into black holes that, themselves, eventually evaporate into radiation, becoming the "Big Bang" of a subsequent temporal iteration (or "aeon") of a single universe encompassing all of reality.
Although the duration of the intervals between aeons cannot be determined (due to a total lack of any form of artificial or natural clock, which would require the presence of mass), the CCC model has some observational support from the CMB, in the form of "anomalous spots of significantly raised temperature", designated as "Hawking points",
which Penrose and several of his collaborators consider to have originated from the evaporation of black holes.
The other model was formulated by Nikodem Poplawski in numerous papers (many of them subsequently published) whose preprints were written between 2010 and 2021, and can be found by his name on Cornell University's << Arxiv >> website.  In Poplawski's torsion-based model, the gravitational collapse of any large rotating star, after its expenditure of its nuclear fuel, results in the materialization of new fermions, whose contact with the vastly larger stellar fermions spins them outward to form a new "local universe" (whose shape Poplawski analogizes to "the skin of a basketball"), in a multiverse that is inflating (expanding at an asymptotically exponential rate).  Our observable region would lie within one of those LU's.
Poplawski's model would represent a version of inflation, although it would not require any of the hypothetical "inflaton" particles which characterize other versions of such quasi-exponential spatial expansion.  As each LU would inherit its arrow of time from a larger "parenting" LU, the multiverse occupied by the LU's would have a prevalent direction of motion:  Such motion has been detected by Cai and by the astronomer Lior Shamir, although the prevalence is faint enough that it may remain controversial.
Because torsion might not clearly exist in a universe or multiverse of "point-like" particles, Poplawski's model was formulated through the use of Einstein-Cartan Theory (itself formulated through conversations between Einstein and the mathematician Cartan in 1929, a few years after the discovery of particulate spin), whereas Penrose's was formulated using the older Theory of General Relativity:  ECT requires that fermions (matter particles) should have a tiny spatial extent (a few orders of magnitude greater than the Planck length), but reduces to GR in vacuum.  Otherwise, the two models seem remarkably similar.
I should mention that, although his verbiage may not have referred specifically to "heat death", Poplawski does mention that the local universes in his multiverse "expand indefinitely", which seems to leave the possibility of heat death occurring in some of them.
