Athel Cornish-Bowden is correct. Any thermodynamicist would (reluctantly) agree that, if the entropy is not a state function, then it is nonsense (nothing). Is there any valid proof that the entropy is a state function? There is none. Here is an oversimplified history of the entropy concept:

If you define the entropy S as a quantity that obeys the equation dS=dQrev/T, you will find that, so defined, the entropy is a state function FOR AN IDEAL GAS: https://socratic.org/questions/is-entropy-state-function-how-prove-it. Clausius decided to prove that the entropy (so defined) is a state function for ANY system. He based his argument on the false assumption that any cycle can be disintegrated into small Carnot cycles, and nowadays this remains the only "proof" that entropy is a state function:

"Carnot Cycles: S is a State Function. Any reversible cycle can be thought of as a collection of Carnot cycles - this approximation becomes exact as cycles become infinitesimal. Entropy change around an individual cycle is zero. Sum of entropy changes over all cycles is zero." http://mutuslab.cs.uwindsor.ca/schurko/introphyschem/lectures/240_l10.pdf

The statement "Any reversible cycle can be thought of as a collection of Carnot cycles" is a blatant lie. An isothermal cycle CANNOT be thought of as a collection of Carnot cycles, a cycle involving action of conservative forces CANNOT be thought of as a collection of Carnot cycles, etc. etc.

Conclusion: The belief that the entropy is a state function is totally unjustified. Any time scientists use the term "entropy", they don't know what they are talking about:

"Von Neumann told me, 'You should call it entropy, for two reasons: In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage." https://en.wikipedia.org/wiki/History_of_entropy

Professor Jos Uffink, University of Minnesota: "I therefore argue for the view that the second law has nothing to do with the arrow of time...This summary leads to the question whether it is fruitful to see irreversibility or time-asymmetry as the essence of the second law. Is it not more straightforward, in view of the unargued statements of Kelvin, the bold claims of Clausius and the strained attempts of Planck, to give up this idea? I believe that Ehrenfest-Afanassjewa was right in her verdict that the discussion about the arrow of time as expressed in the second law of the thermodynamics is actually a red herring." http://philsci-archive.pitt.edu/313/1/engtot.pdf