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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?

user8736288
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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.