Why is entropy a state variable even for irreversible path?

[goodphy]

Hello.

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.

 

[Chestermiller]

Suppose you had an irreversible process path that took your system from thermodynamic equilibrium state A to thermodynamic equilibrium state B. How would you determine the change in entropy for your system?

 

[Chestermiller]

Here is a cookbook recipe for determining the change in entropy for a system that has experienced an irreversible process: https://www.physicsforums.com/insights/grandpa-chets-entropy-recipe/