Suppose that the ideal gas is expanding adiabatically from the state $(P_1, V_1, T_1)$ to the state $(P_2, V_2, T_2)$
I think this process can be allowed to happen reversibly or irreversibly, but then I face a puzzling contradiction regarding entropy change ($\Delta S$).
If the process occurred reversibly, $\Delta S = 0$ since there are no heat transfer and no entropy generation.
If the process occurred irreversibly, $\Delta S > 0$ since there is entropy generation by the irreversibility of the process.
However, because entropy is a state function it cannot be zero and non zero for the two fixed chosen states $(P_1, V_1, T_1)$ and $(P_2, V_2, T_2)$