Is a financial fine imposed by public libraries for overdue books considered a monetary ta'zir?

Punishment by financial penalty (ta'zir bi al-mal) is only to be carried out by the ruler (wali al-amr) or his deputy. As for libraries imposing fines for overdue books, this is not a financial punishment (ta'zir bi al-mal). Rather, it is a fee for the continued use of the book after the loan period has expired, and it serves as an encouragement to fulfill conditions. This is similar to the opinion of some scholars who say that if someone borrows an animal to travel to a certain town but then goes beyond it, he must pay the equivalent rent for the additional distance.