I could have sworn I wrote something about this when the first movie came out, but I cannot find my comment on the board.
Elia Cmiral composed the scores to Atlas Shrugged Part 1 and Atlas Shrugged Part 3. Chris Bacon composed Part 2 and did not use any of the themes from Part 1, though Cmiral did revisit themes from 1 for 3.
There is a recurring motif in 1 and 3 that is somewhat reminiscent of "The Future Ain't What It Used To Be." I do not think Cmiral was plagiarizing Jim by any means, the bits are different enough to be a coincidence. However, I find it interesting that Atlas Shrugged is about a dystopian future, and so is "The Future..."