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Reduced distribution function

Definition

$ \rho $ … Classical probability density function
$ N \equiv \mathrm{dim}(\mathcal M) $
$s < N$
$f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d p_{s+1}\cdots \mathrm d q^N \mathrm d p_N$

Discussion

We also set $f_N:=\rho$, but that's just introduction of different notation.

Relevant for discussions of kinetics on the intermediate level $f_1$ and $f_2$. And maybe $f_3$ if you're mad enough.

Parents

Requirements

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