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So I've been reading this answer.

The question boils down to how we calculate pressure on microscopic level in absence of a rigid boundary. In statistical physics pressure by a gas on a boundary is calculated from the change of momentum of atoms/molecules reflected by the boundary. In absence of a boundary one could suggest scattering against other molecules - but then, what is the difference between mascroscopic (bouyancy, convection) microscopic (diffusion, heat conduction) behavior of a gas?

It seems to me that one can start from BBGKY hierarchy and derive all properties pertaining to a gas?

How does one derive that the equation of motion in the continuum limit should be:

$$ \vec F = P \vec A$$

starting from BBGKY hierarchy?

More Anonymous
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1 Answers1

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According to your link $\mathbf{F}_{i}=-\frac{\partial \Phi_{i}^{ext}}{\partial q_{i}}$

the interaction potential $\Phi_{i,j} $ is assumed to be zero.

we know that: $F=-\frac{\partial E}{\partial r}\;\;\;(1)$

taking the average over this equality, we find: $\bar{F}=-\frac{\partial E}{\partial V}dS\;\;\;\;(2)$

so $\;\;P=-\frac{\partial E}{\partial V}\;\;\;\;(3)$, Pascal's law and: $F=PdS $

(1),(2),(3) L.Landau, E.Lifchitz statistical physics first part,volume V.

The Tiler
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