entropy change of an irreversible process

flasherffff

i cant seem to get something in classical thermodynamics
entropy is a state function of a system,that means it only depends on the state of a system not time or path.
if i have an irreversible process between state 1 and state 2, and back to state 1, and i want to know the entropy change of the system after this cycle.
how can the entropy increase if im back to the same state which means the same entropy with zero change

my book says the entropy change of an irreversible process is greater then that of a reversible process
but how?

Gear300

Its the total entropy change (environment and system) that its accounting for. When the system goes back to its original state in an irreversible process, the environment records the process.

Andrew Mason

The system returns to its original state but the surroundings do not. There is no change in entropy of the system. But the entropy of the surroundings increases if the process between those two states was not reversible.

If the process was reversible, the entropy of the surroundings remains unchanged even though they end up in a different thermodynamic state.

AM