I Single-particle phase spaces for a system of interacting particles

[Riotto]

TL;DR Summary

For a system of interacting particles, is it possible to define single-particle phase spaces? If not, why?

For a system of interacting particles, is it possible to define single-particle phase spaces? If not, why?

 

[mfb]

If you magically fix the states of other particles - but then you are at a one-particle system and the questio becomes trivial.

 

[hilbert2]

You can also form a phase sub-space where the coordinates are weighted averages from the coordinates of several different particles. Or anything that linear algebra allows. Sometimes it's possible to make an approximation that the motion of some degrees of freedom is independent from others, for instance a really heavy harmonic oscillator, with large spring constant, weakly coupled to low-mass oscillators.