Entropy in the Big Bang

“The primordial fireball was a thermal state a hot gas in expanding thermal equilibrium. But the term ‘thermal equilibrium’ refers to a state of maximum entropy. However, the second law demands that in its initial state, the entropy of our universe was at some sort of minimum, not a maximum!” How would you resolve this paradox raised by R. Penrose?

Answer

We quote from the reference listed. The “standard” answer attempting to explain the paradox is:

True, the fireball was effectively in thermal equilibrium at the beginning, but the universe at that time was very tiny. The fireball represented the state of maximum entropy that could be permitted for a universe of that tiny size, but the entropy so permitted would have been minute by comparison with that which is allowed for a universe of the size that we find it to be today. As the universe expanded, the permitted maximum entropy increased with the universe’s size, but the actual entropy in the universe lagged well behind this permitted maximum. The second law arises because the actual entropy is always striving to catch up with this permitted maximum.

This answer cannot be correct if the universe will eventually suffer a “big crunch,” for then the argument would apply again in the reverse direction! We are at an impasse.