stat mech overview sci2
TRANSCRIPT
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N
f
p
q
q
p
Rf
f
p
q
Rf
i
pi
H(q, p)
pidpidt
=H
qi;
qi
dqidt
= H
pi,
i [1, f]
(q, p)
M,
(q, p)
fi=1dqidpi (q, p) (q, p)
fi=1dqidpi
(q, p)
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(q,p,t)
ddt
= 0.
t
+f
i=1
qi
qi+ pi
pi
= 0
)=
t+
fi=1
qi
Hpi
+ pi
Hqi
= 0.
(p,q,t)t
= 0
s.s =(H(q, p))
N V E
N
V
T
V
T
N V E
(N , V , E )
N V E = constant N V E(q, p) 1
,
(N , V , E )
1/(N , V , E )
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N V T
T
E
NV T(q, p)
exp(H(q, p))
= (kBT)1
T
kB
N
V
T
ZN(V, T) =
dq
dp exp(H(q, p))
N V T(q, p) = exp (H(q, p)) /Z
V T
E H
V T(q,p,N) exp((HN(q, p) N))
V T =
N
dq
dp exp((HN(q, p) N)) =
N=0eNZN(V, T)
|(ra, rb)|
2 = |(rb, ra)|2
(ra, rb) = (rb, ra)
(ra, rb) = (rb, ra)
(r1, r2 = r1) = 0
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r
nr r r
r
r
nr =N;
r
nrr =E.
{n1, n2, n3, }
nr = 0 1 nr = 0, 1, 2, 3, 4,
P({n1, n2, }) exp
r
nrr
r
nr
=
r
exp[nr(r )] .
P({n1, n2, }) =
r
pr(nr); pr(nr) exp[nr(r )]
nr pr(nr) = 1,
pr(nr) =exp[nr(r )]
S ,
S=
nr
exp[nr(r )] ,
nr = {0, 1} S
SFD, r = 1 + exp [(r )] = 1 +xr xr = exp [(r )]
nr = {0, 1, 2, 3, } S
SBE, r = 1 + xr+ x2r+ x3r+ = 11xr .
SFDBE , r = (1 xr)1
F D
r
pFDBE
, r = xnrr
(1 xr)1 , xr = exp [(r )] .
nr =
nrnrpr =
0x0r+1x
1r
(1+xr)
, nr = {0, 1}
0x0r+1x1r +mx
mr +
(1xr)1 , nr = {0, 1, 2, 3, 4
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