DOC.
3
45
The
number
of
systems
whose
state
variables
lie in
the
infinitesimally
small
region
g
before the
change
is
given by
the formula
dN
-
Ae
dp^...dpn
;
here
we are
free
to choose
the
arbitrary
constant
in
V
for
each
given
h
and
Va
such
that
A
will
equal
unity.
We
shall
do
this
to simplify
the
calculation
and
shall call this
more
precisely defined function
V*.
It
can
easily be
seen
that
the
value of the
quantity
we
seek
will
be
(2)
aV*dpn
=
1/NV*dp1...dqn,
~f
dp~
=
~I
o{e_2h(V+L)}.rdp1...dq
where
the
integration
should extend
over
all values of the variables,
because
this
expression
represents
the increase
of the
mean
potential
energy
of the
system
that
would
take effect if the distribution of
states would
change
in
conformity
with
6V*
and
6h,
but
V
would
not
change
explicitly.
Further,
we
obtain
(3) " "Py
iKh
lwdpp
=
iKi\
S{e'2hiV*+L)}-h.V.dp1...dqJl
=
4KS[hV]
-
^
[
e~2h{V*+L)6[hiq dpv..dq
.
Here and in
the
following
the
integrations have
to
be extended
over
all
pos-
sible
values
of
the variables. Further, it should
be
kept
in
mind
that
the
number
of
systems
under consideration
does
not
change.
This
yields
the
equation
S(e
24(P*+-£)
)dpy
.
.dq^ =
0
,
or
e
-2
h{V*+L)
6(hV)dp^..
.dqn
+
6h
e
f
-2
h(V*+L)
S(L)dpy
.
.dqn
=
0
,
or
(4)
4k
-2h(F*+L)
at
N
6(hV)dp^..
.dqn
+
4kL6Ii
=
0
.
[35]
[36]
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