Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multisymplectic Theory of Balance Systems and Entropy Principle   In this paper we are presenting the theory of balance equations of the
Continuum Thermodynamics (balance systems) in a geometrical form using
Poincare-Cartan formalism of the Multisymplectic Field Theory. A constitutive
relation $\mathcal{C}$ of a balance system $B_{C}$ is realized as a mapping
between a (partial) 1-jet bundle of the configurational bundle $\pi:Y\to X$ and
the dual bundle similar to the Legendre mapping of the Lagrangian Field Theory.
Invariant (variational) form of the balance system $B_{C}$ is presented in
three different forms and the space of admissible variations is defined and
studied. Action of automorphisms of the bundle $\pi$ on the constitutive
mappings $C$ is studied and it is shown that the symmetry group $Sym(C)$ of the
constitutive relation $C$ acts on the space of solutions of the balance system
$B_{C}$. Suitable version of Noether Theorem for an action of a symmetry group
is presented with the usage of conventional multimomentum mapping. Finally, the
geometrical (bundle) picture of the Rational Extended Thermodynamics in terms
of Lagrange-Liu fields is developed and the entropy principle is shown to be
equivalent to the holonomicy of the current component of the constitutive
section.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio