Lower Bound for Comparison-based sorting algorithms We know that the lower bound for comparison-based sorting algorithms is Ω(nlogn), where logn being the binary logarithm of n. But what about for the best-case scenario of the bubble sort, which takes O(n) time? Of course, n is faster than nlogn. Why is that?

However, I don't know if this bound only applies for the worst-case scenario. I haven't ever learned the lower bound for the best- or average-case scenario. Is it different from the other?

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The lower bound of sorting algorithm comparison based is $O(nlogn)$.
The best case lower bound is $O(n)$ which comes from fact that you need to check if numbers are sorted, so you traverse all of them to find out if they are ordered.

The lower bound is applied to all instances of problem, not just lucky particular case.