  For hyperbolic systems of conservation laws, uniqueness of solutions is still
largely open. We aim to expand the theory of uniqueness for systems of
conservation laws. One difficulty is that many systems have only one entropy.
This contrasts with scalar conservation laws, where many entropies exist. It
took until 1994 to show that one entropy is enough to ensure uniqueness of
solutions for the scalar conservation laws (see Panov [Mat. Zametki,
55(5):116--129, 159, 1994]). This single entropy result was proven again by De
Lellis, Otto and Westdickenberg about 10 years later [Quart. Appl. Math.,
62(4):687--700, 2004]. These two proofs both rely on the special connection
between Hamilton--Jacobi equations and scalar conservation laws in one space
dimension. However, this special connection does not extend to systems. In this
paper, we prove the single entropy result for scalar conservation laws without
using Hamilton--Jacobi. Our proof lays out new techniques that are promising
for showing uniqueness of solutions in the systems case.
