  A general understanding of optimal control in non-equilibrium systems would
illuminate the operational principles of biological and artificial nanoscale
machines. Recent work has shown that a system driven out of equilibrium by a
linear response protocol is endowed with a Riemannian metric related to
generalized susceptibilities, and that geodesics on this manifold are the
non-equilibrium control protocols with the lowest achievable dissipation. While
this elegant mathematical framework has inspired numerous studies of exactly
solvable systems, no description of the thermodynamic geometry yet exists when
the metric cannot be derived analytically. Herein, we numerically construct the
dynamic metric of the 2D Ising model in order to study optimal protocols for
reversing the net magnetization.
