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Phase Space

What do we need to characterize a system in an ensemble?

Classical answer: coordinates and momenta of all particles!

N particles, each has 3 coordinates and 3 momenta--6N-dimensional space. This is called phase space . Each system is a point in this space. The time evolution is a flow in the phase space!

$\begin{figure*} \InputIfFileExists{phase_space.pstex_t}{}{}\end{figure*}$

Ensembles are regions in phase space

Mechanical approach:: Describe each trajectory in phase space
Statistical approach:: Describe the flow in the phase space, averages, distribution, deviations, etc. This is the problem we will discuss in this course.