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My textbooks have explained why Enthalpy, Entropy, Internal Energy, Gibbs Free Energy are state functions or path functions only intuitively and with examples. But that never fully satisfied me. Is there any mathematical way to prove whether a given function is a state function or path function?

user281837
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    Yes, perform a path integral over a closed path. The resulting integral should be zero for a state function, independently of path. Not so for the path function. See https://chemistry.stackexchange.com/questions/22171/why-is-du-an-exact-differential-and-dq-an-inexact-differential/22172#22172 – Buck Thorn Apr 18 '21 at 14:50

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