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There is the Gibbs theorem in thermodynamics, according to which the entropyof the mixture of ideal gases is equal to the sum of the entropies of thecomponents of the mixture. J. W. Gibbs proved this by a mathematical derivationfrom the beginnings of thermodynamics and the laws of ideal gases, inparticular Dalton's law. This message shows that this proof is mathematicallyincorrect. It is also shown that the Gibbs theorem cannot be derivedmathematically from Dalton's law.

On the incorrectness of the proof of the Gibbs theorem on the entropy of a mixture of ideal gases, which was given by J. W. Gibbs