I would have thouth you would have said zero since you you left open the posibility of positive entopy change in your statement. Nice try, though. Strike ONE!
And we don't all have math fonts turned on.
Math fonts won't get you from reversible to irreverible cycles. Srike TWO!
I am open to a civil, moderated education on path variables and reversible cycles, please proceed. I suspect reversible cycles apply to open systems, because how could entropy increase over time in a closed system? See you later.
Let me quote from the same previous text:
"These equations (entropy) can be summarized by the statement that a natural process always takes place in such a direction as to cause an increase in the entropy of the system plus environment. In the case of an isolated system it is the entropy of the system that tends to increase."
Strike Three. You are OUT!