Taking [tex] S=kln\Omega [/tex] to define entropy, it follows immediately that [tex] \frac{dS}{dt} \geq 0 [/tex] holds as a statisical law so long as we assume equal a priori probabilities for each microstate. It seems that so long as we use the Bayesian interpretation of probability, the second law does not need to be postulated but rather can be proved.(adsbygoogle = window.adsbygoogle || []).push({});

Also, would it be possible to prove Carnot's theorem in the following way: The area enclosed in a P,V graph for a material undergoing a cyclic process between heat reservoirs of given temperatures tells us the work done in the cycle, from which we can calculate the efficiency. Couldn't we set up a functional which tells us the efficiency of a given path in the P,V diagram, and maximise it using functional differentiation to tell us the most efficient path? And then from this couldn't the second law be deduced, since carnot's theorem is a statement of the second law?

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# Does the 2nd law of thermodynamics need to be postulated?

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