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Origin and justification for stating the second law of thermodynamics as $dS=d_{\rm{e}}S+d_{\rm{i}}S$?

The second law of thermodynamics is sometimes stated as: $dS=d_{\rm{e}}S+d_{\rm{i}}S$ with : $dS$, the variation of entropy of the system; $d_{\rm{e}}S$, the entropy exchanged with or supplied to the ...
2 votes
1 answer

How did Gibbs discover Gibbs entropy?

I have read and I think that I agree with the idea that if we have to choose probability distribution for an unknown system then it is a good idea to choose a distribution that has the least bias. I ...
4 votes
0 answers

In which work was Boltzmann's entropy originally introduced?

I get an impression from this enyclopedia entry that the primary source of the Boltzmann entropy equation $S = k \log W$ might be 1866, Über die Mechanische Bedeutung des Zweiten Hauptsatzes der ...
4 votes
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In which work was Gibbs' Inequality introduced?

Gibbs' inequality $$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$ is such a popular thing that I cannot find where it was introduced. My findings I ...
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1 answer

How did Carnot come up with the idea of Carnot Engine being the most efficient engine?

I am not asking the proof of why the Carnot Engine is the most efficient engine. I wish to know the history of the development of idea of the most efficient engine. I wish to know how Carnot came up ...