APPENDIX
A 585
derived
(a
similar discussion
occurs
in
Einstein’s
lecture notes
for
a course on
kinetic
theory
in 1910
[see
Vol.
3,
Doc.
4,
pp.
234-235]).
This
is next
applied
to
osmotic
pressure
and diffusion.
Finally,
two
topics
of fundamental
importance
are
discussed: the derivation of
the
second law of
thermodynamics
from statistical
mechanics,
and Boltzmann’s
princi-
ple.
The second law
is
derived from the invariance of the
norm
of the distribution
function for small variations of the
temperature
and of the
parameters determining
the
energy.
This invariance is shown
to
imply
that
dQ/T
is
a
total differential. An
ex-
pression
for the
entropy
is
derived
as
well. Boltzmann’s
principle
and the relation be-
tween
irreversibility
and
probability
are
discussed in the
final
lecture. The discussion
is illustrated with
an
example
that Einstein had also used
on
earlier occasions
(see,
in
particular,
Einstein
et
al.
1914,
pp.
355-356):
a
fluid
containing
a
particle
whose
density
is
greater
than that of the
surrounding
fluid.
Although
the
particle
will fall
most
of
the time,
because lower
positions
have
higher
probability,
it
will also
some-
times
move
upward,
thus
illustrating
the statistical
nature
of
irreversibility.