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Yes, your three-body expression is consistent with the BBGKY hierarchy. Regarding $n$-body correlations, there may be a way to express the collision integrand in terms of $g$ and $f$ functions, but I do not know it and can not remember ever seeing one. That said, I'll heartily upvote any answer that manages to write it out. Most treatments of the problem ...

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What makes water boil/evaporate is the thermodynamic concept derived from the first and second law of thermodynamics. You can read this article to find out the derivation from entropy to the Clapyeron equation. http://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation#Derivation_from_state_postulate \frac{\mathrm{d} P}{\mathrm{d} T} = \frac ...

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First law of thermodynamics states that the change in internal energy, $dU$, of a system is equal to $\delta Q + \delta W$. The only way to separate the contributions from the two is to arrange the experiment so that one of the quantities is zero. If the change is adiabatic so that there is no heat exchange, $\delta Q = 0$ and hence $dU = \delta W$. On the ...

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