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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?