To get some easy equations we need to reduce from \(\Gamma\) space to \(\mu\) space.

Two Spaces | \(\Gamma\) space | \(\mu\) space |
---|---|---|

Dimensions | \(6 N\) | \(6\) |

State of system | A point | \(N\) points |

Probability density | \(\rho(q^n_i, p^n_i; t)\) | \(f_n(q_i,p_i; t)\) | |

Observables | Difference in the integration | |

EoM | Liouville equation or Von Neumann equation | BBGKY Hierarchy |

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