That quote is not exactly correct, there are plenty of evolution equations which are not time-reversible beginning with the linear heat equation. If you look at

That quote is not exactly correct, there are plenty of evolution equations which are not time-reversible beginning with the linear heat equation. If you look at the solution given by convolution (usually taught in first PDE course) you see that this equation has infinite speed of propagation. Any parabolic/dissipative equation is not time-reversible (which is analogous to addition not being reversible... dissipation involves an averaging process). Elsewhere the author says "all fundamental evolution equations in physics are time-reversible." By fundamental I'm assuming she means: Maxwell's equations, Einstein's field equations and the Schrodinger equation.