  We present and develop several nonlinear energy conditions suitable for use
in the semiclassical regime. In particular, we consider the recently formulated
"flux energy condition" (FEC), and the novel "trace-of-square" (TOSEC) and
"determinant" (DETEC) energy conditions. As we shall show, these nonlinear
energy conditions behave much better than the classical linear energy
conditions in the presence of semiclassical quantum effects. Moreover, whereas
the quantum extensions of these nonlinear energy conditions seem to be quite
widely satisfied as one enters the quantum realm, analogous quantum extensions
are generally not useful for the linear classical energy conditions.
