We study mechanical problems with multiple solutions and introduce a
thermodynamic framework to formulate two different selection criteria in terms
of macroscopic energy productions and fluxes. Studying simple examples for
lattice motion we then compare the implications for both resting and moving
inhomogeneities.Comment: revised version contains new introduction, numerical simulations of
Riemann problems, and a more detailed discussion of the causality principle;
18 pages, several figure
