54 FOUNDATIONS OF
STATISTICAL PHYSICS
Einstein's
later interests:
(3)
the
interpretation
of
the constant
K
(again,
in
effect,
Boltzmann's
constant) as a measure
of
the
thermodynamical stability
of
a system; (4)
the
derivation of
an energy
fluctuation formula that heralds
Einstein's
subsequent
investiga-
tions
of
Brownian motion and other fluctuation
phenomena;
and
(5)
the
application
of
this
formula to fluctuations in the
energy
of
black-body
radiation within
a
small
cavity,
result-
ing
in the derivation
of
an analog
to
Wien's
displacement
law,
with
a
numerical factor that
agrees
to
an
order
of
magnitude
with the
empirical
results.[68]
The last
of Einstein's
papers
devoted
solely
to the foundations
of
statistical
physics
by
no means represents
the last
of Einstein's
contributions to the
discussion of
the
issues
raised in these
papers.
In the
years
after
1904,
Einstein continued to comment
upon
these
issues,
but
always
in the context
of
specific problems, or applications
in
other
areas.
For
example,
Einstein's
use
of
the Boltzmann
principle,
S
=
k.log
W,
in his
papers on
the
quantum hypothesis,
led him to think about the
principle's
proper
interpretation,
and
to
disagree
with
Planck about the
right way
to count
"complexions" ("Komplexionen").[69]
Many
of Einstein's
arguments
for
defining
probabilities
in
physics as
time
averages
are
found in his
papers
on
the
quantum hypothesis.[70]
His
continuing
interest in
fluctuations,
and
in
the attendant
question
of
the limits
of
validity
of
macroscopic
thermodynamics,
is
evident
in his
papers on
Brownian motion and critical
opalescence.[71]
In the
latter
paper,
Einstein also laid the foundations
of
what
later
became known
as
statistical
thermo-
dynamics.[72] Finally,
his
papers on quantum
statistics in 1916-1917 and
1924-1925
are
still
investigating
the
changes
in
the foundations
of
statistical
physics
required
by
the
quantum hypothesis.[73]
Further
evidence
of Einstein's
interest
in the foundations
of
statistical
physics
is
pro-
vided
by
the lectures
on
statistical
physics
that he delivered at various universities
between
1908 and
1918.[74]
It
is
noteworthy
that the
point
of
view
presented
in
these lectures
is
virtually
identical
to
that
developed
in
his first three
papers on
the
subject
(Docs. 3, 4,
and
5).
The
presentation
is
more sophisticated, incorporates
the Gibbsian
terminology
in dis-
cussions
of
the microcanonical and canonical
ensembles,
and
displays a
clearer under-
standing
of
the nature
of
the
required ergodicity assumptions.[75]
But,
in
spite
of
the fact
[68]
For
a
discussion
of
black-body
radiation
and the Wien
displacement
law,
see
the editorial
note,
"Einstein's
Early
Work
on
the
Quantum
Hypothesis,"
p.
135.
[69]
See
especially
Einstein 1907a
(Doc. 38),
§ 1,
and
Einstein
1909b
(Doc. 56), p.
187. For
a
discussion
of
this
dispute
with
Planck,
and
of
Einstein's
views
on
probability
in
this
context,
see
the editorial
note,
"Einstein's
Early
Work
on
the
Quantum
Hypothesis,"
pp.
137-139.
[70]
See the
papers
cited above in note 63.
[71] See, e.g.,
Einstein 1905k
(Doc. 16),
Ein-
stein 1906b
(Doc. 32),
Einstein 1907b
(Doc.
39),
Einstein
1910c,
and the editorial
note,
"Einstein
on
Brownian Motion,"
pp.
206-222.
[72]
See Einstein
1910c,
which
was partially
anticipated
in Einstein 1907b
(Doc. 39).
For
a
discussion
of
statistical
thermodynamics,
see
Tisza
and
Quay
1963.
[73]
See Einstein 1916a,
1916b, 1924,
1925a,
and 1925b.
[74]
See note 3. In
Berlin,
Einstein
was
not
obliged
to lecture
on any
topic (see
Kayser
1930,
p.
124),
yet
chose to lecture several times
on topics
in statistical
physics.
[75]
See, e.g.,
Walter
Dällenbach's
notes for
Einstein's
lectures
on
"Molekulartheorie der
Wärme"
at
the
ETH, summer
semester
of
1913
(SzZE
Bibliothek,
Hs
304:1224),
p.
15,
where
the
equivalence
of
time and ensemble
averages
is
discussed.