1 8 0 D O C U M E N T 4 2 J U N E 1 9 2 0
My comprehension of your remarks is hampered by my not rightly knowing
anymore what I wrote down for Edith at the
time.[4]
It appears certain to me, too,
that
should be interpreted as the components of the pressure tensor (or momentum ten-
sor), and that therefore, in the stationary state
must apply. Otherwise the principle of momentum conservation is
violated.[5]
In carrying out the variation, under no condition may be regarded as
given.[6]
The question that the variational principle is supposed to solve is the fol-
lowing:
What is the most likely velocity distribution within an unmoving gas of a given
density and a given energy, when it is known that the same gas is transporting a
given heat
flow?[7]
This then yields the pressure anisotropy. Once this distribution
is obtained, it furnishes the ’s, by which the problem is solved. One can arbi-
trarily define the temperature, you know, by the equation .
The ruse is, of course, that—instead of determining the anisotropy’s dependence
on the inhomogeneity of the gas’s motion through subtle calculations in statistical
mechanics, using Maxwell’s method—one introduces an arbitrary hypothesis
(most likely distribution for the given energy flow).[8] But I am convinced that by
strict scrutiny of the outcome, this ruse can subsequently be vindicated.
I no longer remember now what I wrote down for Edith at the time, and it is cer-
tainly possible that I was somehow mistaken in the last part of the consideration,
which I recall the least clearly. However, I would proceed in the following manner:
The variation argument delivers as the final result for a heat flow (T = abs. temp.)
parallel to the x axis:
(1)
where and no longer contain . Additionally, it generally holds that:
m f d
1
d
2
d
3
T =
T
x
------------
1 3 –
0=
T11
T
3 T
1
2
2
2
3
2
+ + =
Txx
x
T
2
+=
Tyy
x
T
2
+=
x
T