96
DOC.
4
FOUNDATIONS OF THERMODYNAMICS
March,
he wrote:
"If
you
look at
my paper
more
closely,
you
will find that the
assumption
of
the
energy principle
and
of
the fundamental atom-
istic
idea alone
does not
suffice for
an explana-
tion
of
the
second
law;
instead,
coordinates
p
must exist
for
the
representation
of
things,
such that
for
every
conceivable total
system
E
dQv/dpv =
0"
("Wenn Du meine Arbeit
ge-
nauer ansiehst,
dann wirst Du
finden,
daß
die
Voraussetzung
des
Energieprinzips
& des ato-
mistischen
Grundgedankens
allein nicht hin-
reicht
zur
Erklärung
des zweiten
Hauptsatzes,
sondern
es
muß
zur Darstellung
der
Dinge
Koor-
dinaten
p
geben, so
daß für
jedes
denkbare
Gesammtsystem
E
dQv/dpv=
0").
After
stating
his
belief
that the
conjunction
of
the
incompres-
sibility
and
stationarity
conditions
is
equivalent
to
the
assumption
that
Hamilton's
equations
are
satisfied, he added:
"If
that
is
true,
then the
en-
tire
generalization
attained in
my
last
paper con-
sists in the elimination
of
the
concept
of
force
as
well
as
in the fact that E
can possess an arbitrary
form
(yet
not
completely)?" ("Wenn
das wahr
ist,
dann besteht die
ganze
durch meine letzte
Arbeit
erzielte
Verallgemeinerung
in
der
Elimi-
nierung
des
Kraftbegriffs
sowie
darin,
daß
E
be-
liebige
Form besitzen kann
(doch
nicht
ganz)?").
Compare
this
comment
to
Einstein's
remark in the letter to Besso of 22
January
1903
to the effect that the
"energy principle"
("Ener-
gieprinzip")
and the
"atomistic
theory"
("atomistische Theorie")
are
alone sufficient
for
the derivation
(see
the editorial
note,
"Ein-
stein
on
the Foundations
of
Statistical
Physics,"
p.
51).
In
later
papers,
Einstein
regularly
im-
posed
the
incompressibility
condition,
citing
the
present paper,
without
noting
that the condition
is not
stated
explicitly
here
(see,
e.g., Einstein
1904
[Doc. 5], p.
358,
and Einstein 1907a
[Doc. 38], p. 180).
It is
possible
that
Einstein's
initial
neglect
of
the
incompressibility
condition
is
the
error
that his
colleague,
Sauter,
claimed to
have
discovered
(see
the editorial
note,
"Ein-
stein
on
the Foundations
of
Statistical Physics,"
p.
47).
[8]
The interaction term
is
assumed
to
be
van-
ishingly
small. See Einstein 1902b
(Doc. 3),
pp.
420-421.
[9]
See Einstein 1904
(Doc. 5),
p.
355,
for
an-
other definition
of
o(E).
[10]
On the
probabilistic interpretation,
see
Einstein
1902b
(Doc. 3), p.
422 and
note
16.
[11]
By
"der
Zustand des
Systems
a"
("the
state
of
the
system
a")
Einstein did not
mean a
specification
of
the
instantaneous values
of
the
P1
...
pn,
but rather the canonical distribution
of
microstates
(Zustandsverteilung)
in
a
virtual
ensemble
of
subsystems
a.
See
p.
177,
line 5.
The
aim
of
the
present
section
(§
4) is
to estab-
lish
a
connection between this state distribution
and
an
observable
measure
of
temperature
for
the
systems X.
[12]
For
Einstein's
introduction
of
the
constant
k,
see
Einstein 1902b
(Doc. 3),
p.
428 and note
25.
[13]
Compare
this
proof
of
this theorem
on
the
separation
of
a system
into two
("Trennungs-
satz") with that in Einstein 1902b
(Doc. 3),
§
5,
and
see
note
20
to
that
paper
for
Hertz's
criti-
cism
of Einstein's
proofs.
[14]
The term
on
the
right-hand
side should be
3/4h.
[15] By
"states"
("Zustände"), Einstein
means
again
canonical distributions
of
micro-
states ("Zustandsverteilungen")
(see
note
11).
[16]
The
term "isopyknisch" ("isopycnic") is
recommended
in Boltzmann
1898b, p.
68, to
designate a change
of
state at
constant
volume.
The term
is
used with the
same meaning
in
Boltzmann
1898a,
§
20.
[17]
This
assumption
was
later criticized
by
Paul
Hertz,
who wrote:
"If
one
assumes,
like
Einstein,
that
more probable
distributions follow
more improbable
ones,
one thereby
introduces
a
special assumption
that is not at all self-evident
and is
very
much in need
of
proof" ("Wenn
man
wie Einstein
annimmt,
daß wahrschein-
lichere
Verteilungen
auf
unwahrscheinlichere
folgen,
führt
man
damit eine besondere An-
nahme
ein,
die keinerlei Evidenz besitzt und
durchaus des Beweises bedarf")
(Hertz,
P.
1910a,
p.
552).
Hertz remarked that the
assump-
tion
is proved
in Gibbs 1902,
p.
150,
and de-
fended this
proof
against
the criticisms in Zer-
melo
1906,
p.
238,
and
Ehrenfest
and
Ehrenfest
1906. After
a personal
discussion with
Hertz,
which, on
Einstein's
account,
resulted in
com-
plete
agreement
between
them,
Einstein wrote:
"I
regard
this criticism
as
completely
correct.
My
derivation had not satisfied
me even
at the
time,
which
is
why
I
gave a
second derivation
shortly
thereafter,
one
that
is also
cited
by
Hertz."
("Ich halte diese Kritik für vollkommen
zutreffend. Meine
Ableitung
hatte mich schon
damals nicht
befriedigt,
weshalb ich kurz
darauf
eine zweite
Ableitung gab,
die auch
von
Hrn.
Hertz zitiert ist.")
(Einstein 1911c,
p.
175).
For
the
"second
derivation,"
see
Einstein 1904