196
DOC. 4 KINETIC
THEORY LECTURE NOTES
If
one
considers
once
and
for
all
a system
with
a given energy
value,
but
assumes
that
the
A can assume
all
possible
values
(piston
does not
exist),
then
dW
=
const
dp1
.....
dpn
If
one
designates W
as
the
probability
of
an
arbitrary
region
Gx,
characterized
by
specific
values
of
k,
we
will
have
W
=
const
.
Gk.
Probability
of
a
A-state
at
given energy equals
the
magnitude
of the
region
in
question.
Hence,
up
to
an inconsequential constant,
we
can
set
5
=
-lg
W.
N
A
[p. 47]
This
is
Boltzmann's
principle.
Proof
that
an
»
small
Microcanonical
and
Canonical Ensemble
dN
=
Adnr
diij
=
AdIIj
• • • •
dl^d^
• •
diz
Energy
of the
whole
between E
and
E
+
A
E-r\
+A
dN'
=
A
ditx dpk
J
dT^ • • • •
dl^
£-il
T
x+A
We
set
J
dT
=
A
*i^(r)
J*dF
=
Y(x)
=
J
ty(x)dx
x
*0
*0
dN' =A
diCj
dTtk
A*i|j(E
-
r\)
Function
i|
is
sought.
1.
Reservoir
is
ideal
gas.
[
const const const
]