D O C . 3 8 5 Q U A N T U M T H E O R Y O F I D E A L G A S I I 3 7 7
The quadratic term is here relatively infinitely small, due to the relatively infinite
size of the remaining system. If the total entropy is denoted as then
because on average it is at equilibrium. One thus obtains for the total
entropy by addition of these equations the relation
(32)
According to the Boltzmann principle, for the probability of the ’s one extracts
from here the law
[12]
From this it follows for the mean square of the fluctuation
(33)
From this, taking into account (29a),
(34)
results. This fluctuation law is completely analogous to the one for Planck’s quasi-
monochromatic radiation. We write it in the form
(34a)
The mean square of the molecules’ relative fluctuation of the kind emphasized is
composed of two summands. The first would have been present alone if the mole-
cules were independent of one another. To this is added a portion of the mean
square of the fluctuation that is completely independent of the mean molecular den-
sity and is determined only by the elementary region ΔE and the volume. It corre-
sponds to interference fluctuations in radiation. One can interpret it likewise in the
case of a gas by suitably assigning to the gas a radiation process and calculating its
interference fluctuations. I shall delve deeper into this interpretation because I be-
lieve that it involves more than a mere analogy.
Σ( S = S°), +
∂Σ
∂Δν
--------- 0, =
Σ Σ
1
2∂Δν
-----------Δν -
∂2S
2. +=
Δν
dW const. eS /ndΔν
e2n∂Δν
1
-----
----------Δν22S2∂
dΔν. = =
Δν 2
κ
∂2S·
∂Δν¹2
–---------¸
©
¨
§
------------------. =
Δν 2 nν
nν2
zν
-----, +=
[p. 9]
Δν
nν¹
-----·
-
©
§
2
1
nν
-----
1
zν
----. +=