In the Karlsruhe physics course one defines the term "substance-like" quantity:
Let my cite the definition from a paper by Falk, Herrmann and Schmid:
"There is a class of physical quantities whose characteristics are especially easy to visualize: those extensive physical quantities to which a density can be assigned. These include electric charge, mass, amount of substance (number of particles), and others. Because of the fundamental role these quantities play throughout science and because such quantities can be distributed in and flow through space, we give them a designation of their own: substance-like."
Are there examples of extensive quantities, which are not substance-like? I think volume is one example, since it seems to make no sense to assign a density to it, are there others?
Now the authors write that a quantity can only be conserved if it is substance-like, let my cite this from an other publication:
F. Herrmann, writes: "It is important to make clear that the question of conservation or non-conservation only makes sense with substance-like quantities. Only in the context of substance-like quantities does it make sense to ask the question of whether they are conserved or not. The question makes no sense in the case of non-substance-like quantities such as field strength or temperature."
So my second question is: Why has a conserved quantity to be substance like? It would be great if one could give me a detailed explanation (or a counterexample if he thinks the statement is wrong).
Are there resources where the ideas cited above are introduced with some higher degree of detail and rigour?