I was under the impression that the entropy of the universe ALWAYS increases. However in my lectures the lecturer stated the second law of thermodynamics as 'In a spontaneous process the entropy of the universe always increases', which seems to imply that this is not so? However when I looked up the second law of thermodynamics, for example here it states
The Second Law of Thermodynamics states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.
Which also seems to imply that the etropy of the universe always increases, not just for spontaneous processes.
Best Answer
I think what your book meant was that, at any given time, there are many spontaneous processes taking place in the universe, and they all cause the entropy of the universe to increase. I think what your professor meant was that each and every spontaneous process that occurs causes the entropy of the universe to increase. For a processes that is reversible for both a system and its surroundings, the entropy change of the universe is zero. There are no processes for the combination of a system and its surroundings where the entropy change of the universe is less than zero.