The second law of thermodynamics states that the thermodynamic entropy of an isolated system (dQ=0, ds=dQ/T=0) is constant. Statistics S=k * In (W), is it an increase?
The second law of thermodynamics : statistical entropy(S=k*In(W)) of an isolated system increases, while thermodynamic entropy(ds=dQ/T) remains constant.
Thermodynamic entropy (ds=dQ/T) is not equivalent to statistical entropy {S=k * In (W)}
Please carefully check the quoted definitions of the second law to make sure that you include the terms "revesible" and "irreversible" in the relevant processes.
"Be more complete and logical." – Well, your statements are incomplete. YOU started this discussion; I'm not here to do your homework.
"Don't solve problems just because of a few trendy terms." – Well, please remember Clausius' famous statement about entropy (cf., e.g., https://en.wikipedia.org/wiki/Clausius_theorem); it is an inequality, so one has to consider two different cases. These two cases are the reversible and the irreversible one. You see? It's not about "trendy terms"!