Why is the lower bound for sorting strings Ω(d + nlogn)? I'm taking an Advanced Algorithms course. I'm currently studying efficient algorithms for sorting strings. In this chapter, it is provided a lower bound for the time complexity of $\Omega(d + n\log{n})$, where d is the sum of the distinguishing prefixes of all the strings in our set S and n is the cardinality of the strings set S. The book says this is the minimum number of comparisons any algorithm must take, and I cannot figure out why. Can you help me? Thank you.
The time complexity you indicated is the lower bound of your specific problem. A lower bound is the worst-case running time of the most optimized TM that recognizes membership in the language.

Lover bound for sorting algorithms is $\Omega(n \log n)$ this means that it is not possible to do better than this and all the sorting cases (instances) may have a temporal complexity $t \geqslant\Omega(n \log n) $. 

For a simple proof of the former lower bound you can take a look at this.