There is no single definition of time that everyone agrees on. Many quantum physicists will say it does not exist. But we obviously feel 'the passage of time' and have different ways of measuring 'it'. Many have tried to define it terms of entropy but that has problems.
Here is an interesting book from a couple of years ago. The author is a distinguished experimental physicist. It is titled 'Now':
https://www.amazon.com/Now-Physics-Time-Richard-Muller/dp/0393285235
He proposes his own definition- but I won't give any spoilers. The book has a good review of the history of the (scientific) debate on the nature of time too, for a general audience (this is not a very quantitative presentation).
Please, spoil away... I have no intentions of buying that book.
What are the problems of defining it in terms of entropy?