Entropy for a closed system
Some people define a "closed system" as one that can exchange neither heat nor work not mass with the broader surroundings.  Others, like us engineers, define a "closed system" as on that can exchange both heat and work with its surroundings, but not mass.  We engineers call a system that can exchange neither heat nor work with the broader surroundings an "isolated system."  Which definition of a closed system are you subscribing to?