This question came to my mind when I was reading the 8th chapter of "Heat and Thermodynamics, 7th edition, Zemansky-Dittman". The book somehow concludes that "Principle of increase of entropy" of the universe is a principle/postulate/axiom and the "Second law of thermodynamics" is just the result of this principle much like in a manner that we say "Principle of conservation of energy" of the universe is more fundamental than the "First law of thermodynamics".

Now this is my question:

Is "Principle of increase of entropy" more fundamental or "2nd law of Thermodynamics" is more fundamental? Which one?