EINSTEIN ON THE FOUNDATIONS OF

STATISTICAL PHYSICS

I

Einstein wrote

only

three

papers

devoted

exclusively

to the foundations

of

statistical

phys-

ics: Einstein 1902b

(Doc. 3),

Einstein 1903

(Doc.

4),

and Einstein 1904

(Doc. 5).

Never-

theless,

these

papers

develop a

number

of

ideas that

play a prominent

role in

Einstein's

subsequent work;

and

they represent

the

beginning

of

a life-long

interest in the

foundations

of statistical

physics, an

interest

amply

demonstrated in other

publications;[1]

in

his

corre-

spondence

with, among others,

Michele

Besso,

Paul

Hertz,

Paul

Ehrenfest,

H. A. Lo-

rentz,

and

D.K.C.

MacDonald; in

the

design

of

instruments for the measurement

of

elec-

trical

fluctuations related to Brownian

motion;[2]

in his

university lectures;[3]

and

in

papers

and diaries

of

friends and

acquaintances.[4]

Einstein's

papers on

statistical

physics

start from within the

Maxwell-Boltzmann

tradi-

tion

in kinetic

theory.

His aim

was

to

fill

what he considered

a gap

in the mechanical

foundations

of

thermodynamics by deriving

the laws

of

thermal

equilibrium

and the

sec-

ond

law

of

thermodynamics

from the

most

general

possible

mechanical

assumptions

and

the

probability

calculus.

Although

there

was

very

little

contemporary response

to

his three

papers,[5]

and Einstein later

downplayed

their

significance,[6]

the harvest

of

results used in

his later work

is

considerable. These include: the derivation

of

an energy

fluctuation for-

mula that

presaged

Einstein's

work

on

Brownian motion and other fluctuation

phenom-

ena;[7]

the derivation

of

an expression

for the

entropy

that Einstein used

repeatedly

in his

[1]

See, e.g.,

Einstein

1910c,

1911h,

1915a,

1916a, 1916b, 1924, 1925a, 1925b;

Einstein

and

Hopf 1910a,

1910b.

[2]

See Einstein 1908a

(Doc. 48),

and the edi-

torial

notes,

"Einstein

on

Brownian Motion,"

pp.

221-222, and Vol.

5,

"Einstein's 'Ma-

schinchen'

for the Measurement

of

Small

Quan-

tities

of

Electricity."

[3]

Einstein lectured

on

statistical

physics

dur-

ing

the

summer

semester

of

1908,

University

of

Bern

(see

the Kreisschreiben

of

6

July

1908,

SzBeSa);

summer

semester

of

1910,

University

of

Zurich

(see

Zürich Verzeichnis

1910a,

p.

22);

summer

semester

of

1912,

German

University

of

Prague (see

Prag

Ordnung 1912a, p. 34);

summer

semester

of

1913,

ETH

(see

ETH

Pro-

gramm

1913a,

p. 14);

winter semester

of

1915/

1916,

University

of

Berlin

(see

Berlin

Ver-

zeichnis

1915b,

p.

48);

and winter semester of

1917/1918,

University

of

Berlin

(see

Berlin

Ver-

zeichnis

1917b, p.

44).

[4]

For

example,

Paul Ehrenfest recorded

in

his

diary

that when he met Einstein for

the first

time in

Prague

in

February 1912, they

immedi-

ately

started

to

discuss the

ergodic hypothesis

(Klein 1970,

p.

176).

And Karl F. Herzfeld

re-

ported

conversations with Einstein

concerning

his

objections to

a

derivation

of

the Boltzmann

principle

in

Herzfeld 1913,

p.

1553.

[5]

Einstein 1902b

(Doc. 3)

and Einstein 1903

(Doc. 4)

are

cited in Boltzmann and Nabl

1907,

p.

549. Martin Klein

(Klein 1970,

p.

46)

re-

ported

that the

young

Ehrenfest read

Einstein's

papers during a

visit

to

Leiden

in

the

spring

of

1903. Ehrenfest later cited Einstein 1902b

(Doc.

3)

and Einstein 1903

(Doc. 4)

in

Ehrenfest

and

Ehrenfest

1911,

pp.

6-7,

80. Einstein 1903

(Doc. 4) is

discussed

at

some length

in

Ornstein

1910 and Lorentz 1916. Paul Hertz

subjected

all

three

papers

to

a

careful

analysis

in

Hertz,

P.

1910a, and

they are

cited

frequently

in his other

papers on

the foundations

of

statistical mechan-

ics,

Hertz, P.

1910b, 1912, 1913a, 1913b,

as

well

as

in his

Repertorium

article, Hertz,

P.

1916.

[6]

See Einstein

1911c, p.

176.

[7]

See the editorial

note,

"Einstein

on

Brown-

ian Motion,"

pp.

206-222.