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Liouville equation
differential equation for the evolution of distribution functions
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Statements
instance of
partial differential equation
of
distribution function
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named after
Joseph Liouville
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studied in
statistical mechanics
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defining formula
d
ρ
d
t
=
∂
ρ
∂
t
+
∑
i
=
1
n
(
∂
ρ
∂
q
i
q
˙
i
+
∂
ρ
∂
p
i
p
˙
i
)
=
0
{\displaystyle {\frac {\mathrm {d} \rho }{\mathrm {d} t}}={\frac {\partial \rho }{\partial t}}+\sum _{i=1}^{n}\left({\frac {\partial \rho }{\partial q_{i}}}{\dot {q}}_{i}+{\frac {\partial \rho }{\partial p_{i}}}{\dot {p}}_{i}\right)=0}
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in defining formula
ρ
{\displaystyle \rho }
symbol represents
distribution function
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t
{\displaystyle t}
symbol represents
time
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q
{\displaystyle q}
symbol represents
generalized coordinate
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p
{\displaystyle p}
symbol represents
generalized momentum
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maintained by WikiProject
WikiProject Mathematics
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Identifiers
Google Knowledge Graph ID
/g/11bc5cxfx6
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Wikipedia
(1 entry)
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dewiki
Liouville-Gleichung
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