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Canonical partition function for an ultrarelativistic gas in a power-law trap
...
Physics
Branch of physics
Statistical physics
Canonical ensemble
Canonical partition function
Classical ideal-gas partition function
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Words: 46
Articles: 1
For energy
p
c
+
U
(
x
)
,
Z
1
=
π
2
(
ℏ
c
)
3
(
k
B
T
)
3
∫
e
−
U
(
x
)
/
(
k
B
T
)
d
3
x
.
(41)
If
U
(
r
)
=
r
2
n
/
V
2
n
/3
, then
Z
1
=
π
(
ℏ
c
)
3
4
V
(
k
B
T
)
3
+
3/
(
2
n
)
I
n
,
I
n
=
∫
0
∞
u
2
e
−
u
2
n
d
u
.
(42)
Consequently
p
V
=
N
k
B
T
, while the mean energy and variance are
N
A
k
B
T
and
N
A
(
k
B
T
)
2
with
A
=
3
+
3/
(
2
n
)
.
Table of contents
46
1
Most likely radius in an isotropic power-law trap
Canonical partition function for an ultrarelativistic gas in a power-law trap
12
Ancestors
(7)
Classical ideal-gas partition function
Canonical partition function
Canonical ensemble
Statistical physics
Branch of physics
Physics
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