motivated by physics, to try to weed out “nonphysical” solutions which have physical entropy decreasing (or according to , mathematical entropy increasing). Remark that requiring more than one entropy condition (for more than one entropy) is impractical – many systems only admit a single nontrivial entropy. In the scalar case, this approach has had tremendous success. In fact, requiring solutions satisfy the entropy condition for at least one strictly convex entropy in $C^1$ is enough to get uniqueness for solutions (see [@panov_uniquness; @delellis_uniquneness; @2017arXiv170905610K]). However, even for the scalar case proving uniqueness with a single entropy condition has proved difficult. The first result [@panov_uniquness] was not until 1994. Furthermore, the first two results [@panov_uniquness; @delellis_uniquneness] use techniques limited to the scalar case. They use the special connection between scalar conservation laws in one space dimension and Hamilton–Jacobi equations: the space derivative of the solution to a Hamilton–Jacabi equation is formally the solution to the associated scalar conservation law. Notably, [@2017arXiv170905610K] gives a proof of the single entropy condition for scalar conservation laws which works directly on the conservation law and utilizes the theory of shifts. Moreover, progress for uniqueness of entropic solutions to *systems* of conservation laws has been slow. 