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The entropy

*S*is a state variable or state function as the integral of

*dS = dQ/T*is a path-independent, provided that the path is reversible process path. However, such a path-independency of the integral breaks down when the path includes irreversible process. So, I guess we can only say that

*S*is a state variable only if there is no irreversible process, but the textbook said S is the state variable no matter the process includes irreversible process or not.

Well..if there is at least one irreversible process path along which the path-independency doesn't hold, how can I justify that S is a state variable?

I would like to get your help to clarify this confusion.