In proving existence of solutions to the Wigner-Poisson (WP) system1,2,3and, indeed, to many systems of partial differential equations, conservation laws are often used to prove that a local solution does not blow up in a finite time interval, and hence is a global-in-time solution. For the (WP) system, one proves1,2a relevant conservation principle referred to as “energy conservation” which takes the form1,2,3