48
FOUNDATIONS OF THERMODYNAMICS
Doc.
4
A
THEORY OF
THE
FOUNDATIONS
OF THERMODYNAMICS
by A.
Einstein
[Annalen
der
Physik 11
(1903):
170-187]
[1]
In
a
recently
published
paper
I
showed
that the
laws of
thermal
equi-
librium
and
the
concept
of
entropy
can
be derived
with
the
help
of the kinetic
theory
of heat.
The
question
that then arises naturally is
whether
the
kinetic
theory
is
really
necessary
for the derivation
of
the
above
foundations
of
the
theory
of
heat,
or
whether perhaps assumptions
of
a more
general
nature
may
suffice. In this article it shall
be
demonstrated that the latter is the
[2] case,
and
it shall
be
shown
by
what
kind
of
reasoning
one can
reach
the
goal.
§1.
On a
general
mathematical
representation
of
the
processes
in
isolated
physical
systems
Let
the
state
of
some
physical
system
that
we
consider
be uniquely
determined
by
very
many
(n)
scalar quantities
P1,P2...pn,
which
we
call
[3]
state
variables.
The
change
of
the
system
in
a
time
element dt
is then
determined
by
the
changes
dp1,dp2...dpn
that the
state
variables
undergo
during
that time
element.
Let
the
system
be
isolated, i.e.,
the
system
considered should
not
interact with other
systems.
It is then clear that the
state of
the
system
at
a
given
instant of time
uniquely
determines the
change
of
the
system
in
the
next
time
element
dt, i.e., the
quantities
dp1,dp2...dpn.
This
statement
is
equivalent to
a
system
of
equations
of the
form
dpi
(1)
-jj-
=
V^PyPj
(i
=
1
...
i
=
n)
,
where
the
Q's
are
unique
functions of their
arguments.
In general,
for
such
a
system
of linear differential
equations
there
does not
exist
an
integral of
the
form