is equal to
mc, where
m
is the atomic mass, while
denotes the Cartesian coordinates of the momentum of an atom.
is a multi-index and
stands for
so that the densities
,
form a hierarchy of moments of increasing tensorial degree up to
degree
N
. Because of the evident symmetry of (27
) there is a relation between
n
and
N, viz.
The kinetic theory of gases implies that the moments (26) satisfy equations of balance of the type (1
) so that the foregoing analysis holds. In particular, we
have (18
) which may now be written in the form
We introduce
and note that by (30
) the phase density depends on the single variable
only. Also (32
) implies that the vector potential has the form
where, by (31),
holds. The field equations (23
) now read
Obviously the coefficient matrices are symmetric in
,
and
is negative definite, provided that
i.e.
must be concave for the system (34
) to be symmetric hyperbolic.
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Speeds of Propagation in Classical and Relativistic
Extended Thermodynamics
Ingo Müller http://www.livingreviews.org/lrr-1999-1 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |