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A general understanding of optimal control in non-equilibrium systems wouldilluminate the operational principles of biological and artificial nanoscalemachines. Recent work has shown that a system driven out of equilibrium by alinear response protocol is endowed with a Riemannian metric related togeneralized susceptibilities, and that geodesics on this manifold are thenon-equilibrium control protocols with the lowest achievable dissipation. Whilethis elegant mathematical framework has inspired numerous studies of exactlysolvable systems, no description of the thermodynamic geometry yet exists whenthe metric cannot be derived analytically. Herein, we numerically construct thedynamic metric of the 2D Ising model in order to study optimal protocols forreversing the net magnetization.

Dynamic Riemannian Geometry of the Ising Model