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So I'm trying to teach myself BBGKY hierarchy. The notes (page 50) have various time scales associated with different processes:

$$ \frac{1}{\tau_C} \sim \frac{\partial V}{\partial \vec q} \frac{\partial }{\partial \vec p}$$

where $V$ is the potential, $\vec q$ is the position and $\vec p$ is the momentum.

I'm confused if it is possible to convert the time scale of collision time between $2$ moelcules $\tau_C$ in terms of macroscopic variables pressure $P$, density $\rho$ and Temperature $T$? It seems possible as one does assume a dilute gas ($\rho$) and room temperature? If so, how?

Frederic Thomas
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More Anonymous
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1 Answers1

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Equilibrium statistical physics ignores the collision processes: they are important in the logical reasoning behind, as the collisions are responsible for establishing the thermodynamic equilibrium, but once in equilibrium quantities like pressure, density and temperature are independent on the collision time.

In non-equilibrium processes the collision time and other related parameters (like the mean free path) are important, since they determine how fast the equilibrium is reached or on what time- and length-scales the assumption of local equilibrium can be applied, etc. Note that different levels of description are possible, all derivable form the BBGKY hierarchy (Boltzmann/kinetic equation, fluid dynamics equations, etc.)

See for related discussions:

Roger V.
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