  We study curve-shortening flow for twisted curves in $\mathbb{R}^3$ (i.e.,
curves with nowhere vanishing curvature $\kappa$ and torsion $\tau$) and define
a notion of torsion-curvature entropy. Using this functional, we show that
either the curve develops an inflection point or the eventual singularity is
highly irregular (and likely impossible). In particular, it must be a Type II
singularity which admits sequences along which $\frac{\tau}{\kappa^2} \to
\infty$. This contrasts strongly with Altschuler's planarity theorem [J.
Differential Geom. (1991)], which shows that along any essential blow-up
sequence, $\frac{\tau}{\kappa} \to 0$.
