Dynamic Riemannian Geometry of the Ising Model

Understand

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.