Minimizing Thermodynamic Curvature and Dissipation in Nonequilibrium Control with Auxiliary Degrees of Freedom

We analyze optimal control trajectories for nonequilibrium processes that minimize excess entropy production while driving transitions between states in minimal time. Such trajectories correspond to geodesics in a Riemannian space whose metric is defined by the Fisher information. For Gaussian processes, this space exhibits negative curvature, which sets a lower bound on entropy production rates. We show that the absolute value of the curvature—and hence dissipation—can be reduced by introducing auxiliary variables that redistribute entropy production across a higher-dimensional manifold. Most of the reduction is achieved by adding two to three auxiliary variables per control variable, providing a compact strategy for improving thermodynamic efficiency. As variance along controlled degrees of freedom increases due to entropy production, variance along auxiliary axes decreases following a power-law relation. These results establish a geometric framework connecting information geometry and nonequilibrium thermodynamics, and suggest general principles for minimizing dissipation in both physical and biological control systems.