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I have a silly question about the phase space. I am confused with the meaning of points in phase space. Does the each point in phase space represent concrete particle of the system, or does it represent the whole state of the system? Our teacher told us, that we use the phase space to describe the development of each particle. It is not right, isn't it?

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A point in phase space represents the state of the whole system.

For example, if you have a system of $N$ particle with coordinates $\vec r_1, \dots, \vec r_N$ and momenta $\vec p_1, \dots, \vec p_N$, its general state will be a point in a $6N$ dimensional phase space:

$$\vec X = (\vec r_1, \dots, \vec r_N, \vec p_1, \dots, \vec p_N)$$

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It represents the "space occuped" by the hypervolume momentum-position of a particle.

If you integrate the three components of position you get volume; if you integrate the three components of momentum you get kind of a momentum volume. If you integrate both together you get the space phase volume

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The quickest way to understand phase space is to read a phase diagram. It may be a PV diagram, or mixture fraction-temperature diagram. So read carefully what x axis represents and what y axis represents. Take PV diagram for example. each particle on the diagram is a pair of pressure (P) and volume (V). It describes the gas system state at that moment. If you, somehow, change (compress or expand) the system state, i.e. its pressure and volume change, the particle moves to another location in the phase space. The confusing part may be the term "particle". It is not one particle in the gas. It is a point in the phase space.

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