DOC.

3

31

whose

coefficients

are

arbitrary

functions of the

p's.

Two

kinds

of

external

forces

shall

act

upon

the

masses

of

the

system. One

kind of force shall

be

derivable from

a

potential

Va

and

shall

represent

external conditions

(grav-

ity, effect of rigid walls without thermal effects,

etc.);

their

potential

may

contain time

explicitly,

but

its derivative with

respect to

time should

be

very

small.

The

other forces shall

not be

derivable

from

a

potential and

shall

vary

rapidly.

They

have to be

conceived

as

the

forces

that

produce

the

influx of heat. If

such

forces

do

not act,

but

Va

depends

explicitly

on

time,

then

we

are

dealing

with

an

adiabatic

process.

Also,

instead

of

velocities

we

will introduce linear

functions

of

them,

the

momenta q1,...,qn,

as

the

system's

state

variables,

which

are

defined

by

n

equations

of the

form

dl

qv=Wv'

where

L

should

be

conceived

as

a

function of the

p1,...,pn

and P1',...,pn'.

§2.

On

the

distribution

of

possible

states between

N

identical adiabatic

stationary

systems,

when

the

energy

contents

are

almost

identical.

Imagine

infinitely

many (N)

systems

of the

same

kind

whose

energy

content

is

continuously

distributed

between

definite,

very

slightly

differing

values

E

and

E+

SE.

External

forces that

cannot be

derived

from

a

poten-

tial shall

not be

present,

and

Va

shall

not

contain the time explicitly,

so

that the

system

will

be

a

conservative

one. We

examine

the distribution of

states,

which

we assume

to be stationary.

We

make

the

assumption

that

except

for the

energy E

=

L +

Va

+

Vi,

or a

[5]

function of this

quantity,

for the individual

system,

there

does

not

exist

any

function of the

state

variables

p

and

q

which remains

constant

in

time;

we

[6]

shall henceforth consider

only

systems

that satisfy this condition.

Our

assumption

is equivalent

to

the

assumption

that the distribution of

states of

our

systems

is determined

by

the

value of

E

and

is

spontaneously

established

from

any

arbitrary initial values of the

state

variables that satisfy

our

condition

regarding

the value of

energy.

I.e., if

there

would

exist for the

[4]