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I didn't read the whole paper but some of the ... by Barney68
early examples are, at best, a bit misleading based on my understanding of entropy.
Entropy is driven by the number of possible states in the system. Disorder is the response of the system to that number of possible states; equilibrium occurs when the likelihood of every possible state is equal and disorder is at a maximum.
If there is no change to the system, entropy remains the same, but so does the number of possible states and with that number of possible states, so does the disorder.
Taking the water example, a given water molecule can be anywhere in the system. That does not change as long as the system is isothermal and sealed or isentropic.