DOC.
14 95
51
=
(p^)
,
52
=
^2^2^
*
If
these
two
systems
are
viewed
as a
single
system
of
entropy S
and
probability
W,
we
have
S
=
Sl
+
S2
=
p(V)
and
V =
f/vVg
•
The
last relation tells
us
that the
states of
the
two
systems
are
mutually
independent events.
From
these
equations
it follows that
p(rvr2) =
+
v2(JF2}
and from
this
we
get,
finally,
=
C lg(Fj)
+
const.
^2^^)
=
^
1§( +
const.
(p(W)
=
C
lg(F)
+
const.
The
quantity
C
is
thus
a
universal
constant;
it follows
from the
kinetic
[30]
theory
of
gases
that its value
is
R/N,
where
the
meaning
of
the
constants
R
and
N
is the
same as
above.
If
S0
denotes the
entropy
in
some
initial
state
of
a
system
considered,
and
W
the relative
probability
of
a
state
having
the
entropy S,
we
obtain, in
general,
S
-
S0
=
J
lg ¥
.
First,
we
deal with the
following
special
case.
Let
a
volume
v0
contain
a
number
(n)
of
movable
points (e.g.,
molecules), which
shall
be
the
object
of
our
consideration.
The space
may
also contain
any number
of
movable
points of whatever kind.
No
assumptions
shall
be
made
about the
law
governing
the
motion
of the points
in
the
space
except
that,
with
regard
to
this
motion,