
150 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
A
pp
1
21
=
()
.
Obviously, the phase “volume” occupied by the ensemble at time t is equal to A
1
:
A
ppEE
ppEE
A
2
2121 2121
=
′
−
′
−
=
−−
=
()()()
.
As time passes, the same set of phase points occupies an equal volume of phase space. Therefore
the phase-point density must remain the same as Liouville’s theorem requires. It is easy to note
that the shape of the successive phase region occupied by the ensemble changes, although the
phase volume is invariant.
5.8 TIME REVERSAL IN MECHANICS (OPTIONAL)
We saw earlier and in Chapter 4 that conservation of energy, momentum, and angular momentu