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∆(D D n + Dn) =−σsf , (118)
∆(Ht + H D t )=n × jel,sf/c. (119)
This also affects the surface entropy production. Starting from
0=∆(Qn + Q D n ) − (µ + c 2 )∆(ρvn − j D n )
=∆(Qn + Q D n +(µ + c 2 ) j D n − (µ + c 2 ) ρvn)
+〈ρvn − j D n 〉∆µ (120)
we have for the conductor-conductor interface
0=∆
(T s+ µc ρc + v · g) vn − Π D nj vj
−T f D n − µc j D c,n + c
E × H + E D × H
· n
and hence
or
+〈ρvn − j D n 〉∆µ, (121)
R sf = −T ∆fn = fn ∆T + 〈ρvn − j D n 〉∆µ
+〈ρc vn − j D c,n〉∆µc − ∆(vj Π D jn)+∆(v · g vn)
+c ∆
E × H + E D × H
· n (122)
R sf = fn ∆T + 〈ρc vn − j D c,n〉∆µc
+
〈vn gj〉−Π D
jn ∆vt,j
+〈ρvn − j D n 〉 ∆µ eff
+c
n ×
E D + E
· ∆Ht , (123)
where µ eff is the same as before, see Eq(117). This expression yields 7 connecting
conditions. So we have a total of 16 boundary conditions for the conductorconductor
interface. They suffice to determine all outgoing collective modes,
7 for each side, the normal component of B + B D , and the lab velocity of
the interface. (Note that the number of the collective modes is reduced in a
conductor, because there are no sq-Modes [4]. Also, the electromagnetic waves
are reduced to magnetic, diffusive modes.)
For the conductor-dielectric interface, Eq(120) implies
0=∆
(T s+ µc ρc + v · g) vn − Π D nj vj − Tf D n
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