Entropy change for an irreversible process

In an adiabatic irreversible process, entropy is generated within the system, and there is no transfer of entropy to the surroundings because heat cannot flow out. Thermally, the surroundings do not even know that anything has happened within the system. So all the generated entropy remains within the system and causes the system entropy to rise, while the entropy of the surroundings does not change.

The only way the entropy of the surroundings can change is if there is heat transfer to or from the surroundings. An adiabatic process is, by definition, a process in which there is no heat transfer between the system and its surroundings. So it is impossible for the entropy of the surroundings to change for an adiabatic process.

For a reversible adiabatic process the entropy of the system also does not change. An example of a reversible adiabatic process is the very slow (quasi-static) expansion or compression of a gas by a piston in an insulated cylinder such that the gas pressure is always in equilibrium with the external pressure. We call this reversible work.

For an irreversible adiabatic process entropy is generated within the system resulting in an increase in the entropy of the system only. An example of an irreversible adiabatic process is the rapid expansion or compression of a gas by a piston in an insulated cylinder such that the gas is not in internal equilibrium during the process. We call this irreversible work.

Hope this helps.