# Entropy as a state function - Is it just a postulate of the second principle?

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?

## 1 Answer

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.

• 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? – user258881 Apr 4 '20 at 6:54
• 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? – user224659 Apr 4 '20 at 8:53
• @FakeMod I tried to clarify. – user224659 Apr 4 '20 at 8:58