I read quite a few questions on this website dealing with the idea of demonstrating that entropy is a state function. None of the answers I read seemed to be fully conclusive. So my question is : is there anything wrong in saying that the second principle postulates the existence of entropy as a state function? Or is there a definitive demonstration showing that from a more restrictive statement of the second principle?
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One complete description of the second law of thermodynamics is:
$\exists \quad S=S(U,V) \quad \textrm{with} \quad dS\geq0$
It indeed contains the existence of entropy as a state function. I for myself don't like the weird historical formulations.
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$\begingroup$ This does not answerthe OP's question of whether the state function property of entropy is just a postulate or does it have a proof? $\endgroup$– user258881Commented Apr 4, 2020 at 6:54
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1$\begingroup$ It doesn't have a thermodynamic proof. It is the foundation of thermodynamics. And it answers exactly what OP is looking for: yes it is part of the second law. Do you want me to show how other statements of the second law follow from this? $\endgroup$– user224659Commented Apr 4, 2020 at 8:53
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$\begingroup$ @FakeMod I tried to clarify. $\endgroup$– user224659Commented Apr 4, 2020 at 8:58