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