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We find, in an intrinsic form, a generalized Rankine-Hugoniot condition withrespect to an entropy density that allows to give the proper interpretation toa formula of Vol'pert reducing the entropy condition on a function with boundedvariation to its expression for generic simple jumps. It also leads to definethe conservation laws only in terms of characteristics and to point out theclass of entropy conditions coming from oriented conservation laws.

Entropy conditions for quasilinear first order equations on nonlinear  fiber bundles with special emphasis on the equation of 2D flat projective  structure. II