Why only reversible adiabatic processes are called isentropic and not irreversible ones?

For both reversible and irreversible adiabatic processes, $$dQ =0$$,and by the definition of entropy $$dS=dQ/T$$, it should imply that entropy is constant for both. Why it is not so?

• Your definition of entropy change is incorrect. It should read $$dS=\frac{dQ_{rev}}{T}$$ where the subscript rev refers exclusively to a reversible path. Dec 22, 2020 at 18:17

In general, you can write that for all processes $$\frac{\delta q}{T} \le dS$$ (Clausius) but in the case of a reversible process you have equality $$\frac{\delta q}{T}|_{rev} = dS$$. If the process is adiabatic then by definition $$\delta q =0$$ hence for the reversible case you have the equality $$dS=0$$, i.e., an isentropic process, but for an irreversible process you can only say that $$0 which is usually verbalized by saying that the entropy can only increase (never decreases) in an adiabatic process that is not reversible.
Although entropy is defined for a reversible transfer of heat as $$dS=dQ_{rev}/T$$, entropy can be generated without heat transfer. An example of an irreversible adiabatic process that generates entropy is the rapid expansion or compression of a gas.