194
DOC.
4 KINETIC
THEORY LECTURE
NOTES
[p. 45]
Canonical Distribution
&
Entropy
dW
=
Ce
*dp1 • • • dpn
=
e
*dpi
dpn
E
dependent on
p1
..
pn,
and
in
addition
on
X1
•••
An.[91]
After
»
small
change
of
state,
canonical
distribution obtains
again.
E
has
now
dE
parameter
X +
dX
We
call this
function E
+
dE.
=
E
+
~~^d^
The
temperature is
9
+
dB.
c
then
has
the
value
c
+
dc.
Before
and
after the
change
we
have
/
dW
=
1.
.
N
3X5")
[
c+dc
6+46
dpj
• •
dPn
'
\e *dPl
dPn "
0
The
first
exponent
can
be
developed
^
dx
c
-
dc
+
-dB
B1
B
The
exponential
function
is
C~
5
1
+
dc
+
-dB
-
T--dX^dx9
02
Thus,
the
above
equation
becomes
J
dc
+
-dB
B2
-Ti-dX
^
BdX
e''sdp1---dpn
= J(/W
=
0
This
can
also
be written
as
Bdc
+
ädB
-
Y*
-dX
=
0
(1)
or
(dc +
d
E
0
^
dX
0
This
equation
holds
for
every
»
small
change
of
state
dE
We
omit
bars
& prove
that
-
=
A
(the
work
added
to
the
system)
dX