DOC.
4
49
i(p1...pn)
=
const.,
which does not
contain the time
explicitly.
However,
for
a
system
of
equations
that represents the
changes
of
a
physical
system
closed
to
the
outside,
we
must
assume
that
at
least
one
such equation
exists,
namely
the
energy
equation
E(p1...pn)
=
const.
[4]
At
the
same
time,
we
assume
that
no
further
integral
of this kind that is
independent
of the
above
equation
is
present.
§2.
On
the stationary
distribution
of state of
infinitely
many
isolated
physical
systems
of almost
equal energies
Experience
shows
that after
a
certain time
an
isolated
system
assumes
a
state
in
which
no
perceptible quantity of the
system undergoes
any
further
changes
with time;
we
call
this
state
the stationary
state. Hence
it
will
obviously be
necessary
for the functions
/i
to
fulfill
a
certain condition
so
that
equations
(1)
may
represent
such
a
physical
system.
If
we now assume
that
a
perceptible quantity
is
always
represented
by
a
time
average
of
a
certain function of the
state
variables
p1...pn, and
that
these
state
variables
p1...pn keep
on
assuming
the
same
systems of
values
with
always
the
same
unchanging
frequency,
then it necessarily follows
from
this
condition, which
we
shall elevate
to
a
postulate, that the
averages
of
all
functions
of the
quantities
p1...pn
must be constant; hence,
in
accordance with the
above,
all
perceptible quantities
must
also
be
constant.
We
will
specify
this
postulate precisely. Starting at
an
arbitrary
point
of time
and
throughout
time
T,
we
consider
a
physical
system
that is
represented
by
equations
(1)
and has the
energy
E.
If
we imagine
having
chosen
some
arbitrary
region
T
of the
state
variables
p1...pn, then
at
a
given
instant of time
T
the values of the
variables
p1...pn
will lie
within
the
chosen
region T
or
outside
it;
hence,
during
a
fraction
of
the
time
T,
which
we
shall call
T,
they
will lie in the
chosen
region T. Our
condition then reads
as
follows: If
p1...pn are
state
variables of
a