Roger Penrose said in "A Road to Reality" (p.701):
“There is a common view that the entropy increase in the second law is somehow just a necessary consequence of the expansion of the universe. This opinion seems to be based on the misunderstanding that there are comparatively few degrees of freedom available to the universe when it is ‘small’, providing some kind of low ‘ceiling’ to possible entropy values, and more available degrees of freedom when the universe gets larger, giving a higher ‘ceiling’, thereby allowing higher entropies."
He concludes thereby:
“There are many ways to see that this viewpoint cannot be correct. It implies for example that, in those universe models where there is a collapsing phase, the entropy necessarily starts to decrease, in violation of the second law.”
“This cannot be the correct explanation for the entropy increase; for the degrees of freedom that are available to the universe are described by the total phase space PUThe dynamics of general relativity (which includes the degree of freedom (which includes the universe’s size) is just as much described by the motion of our point x in the phase space PU as are all the other physical processes involved. This phase space is just ‘there’, and it does not in any sense ‘grow with time’, time not being part of PU. There is no such ‘ceiling’, because all states that are dynamically accessible to the universe (or family of universes) under consideration must be represented in PU. It may take some while for x to reach some large coarse-graining box from some given smaller one, but the notion of an ‘entropy ceiling’ is inappropriate.”
My question would be: how deeply are expansion and thermodynamic "forces", like most prominently entropy connected? Is Penrose right once again and if yes, how so?