Question

Can the entropy of a part of a closed system become less than the initial entropy of the entire system?

Answer 1

The second law of thermodynamics requires that, in general, the total entropy of any system can't decrease other than by increasing the entropy of some othersystem. Hence, in a system isolated from its environment, the entropy of that systemtends not to decrease.

Answer 2

yes , Entropy always increases (or at best, stays constant) in a closed system. It does not matter what the system is made of; matter, antimatter, light, whatever. Loosely speaking, entropy is a measure of disorder in a system; left to its own, every system heads from more orderly (i.e., less probable) configurations to less ordered (more probable) configurations.

In a system that's not closed, entropy can decrease.