Does the thermodynamic arrow reverse in a recollapsing universe
In plain words
If a universe stopped expanding and fell back together, would entropy keep rising until the crunch, or would the direction of time flip? The answer shows whether the arrow of time is tied to cosmic expansion or only to the initial state.
Precise statement
For a closed Friedmann universe with matter and radiation that recollapses, with low-entropy initial conditions at the big bang and no imposed final condition, determine whether coarse-grained entropy (including a gravitational contribution) increases monotonically to the big crunch, and whether two-time boundary conditions with low entropy at both ends are consistent with the statistical mechanics of matter plus gravity. Answer: yes or no for monotonic increase, with conditions.
What would settle it
A statistical-mechanical calculation of entropy evolution through recollapse for a specified matter content, including structure formation and black holes.
Status in the literature
Hawking argued for reversal in 1985 and later withdrew the claim; no complete statistical treatment exists.