SFU MOCAD Seminar: Jordan Sawchuk

Minimizing energy dissipation in driven stochastic systems is a fundamental goal in nonequilibrium thermodynamics. In the linear-response (slow driving) regime, this becomes a problem of Riemannian geometry: The control space is equipped with a metric (the "generalized friction tensor") and optimal protocols are geodesics. This talk follows one physicist's (nearly) random walk through the mathematical landscape in an effort to understand this thermodynamic geometry.

I will demonstrate that the generalized friction tensor is deeply connected to the network topology of the controlled system, revealing unexpected links to previously established graph-theoretic geometries. Treating the friction tensor as a metric on the probability simplex, I show that the metric tensor is directly related to the mean first-passage times between states, and that dissipation is equivalently seen as a discrete $L^2$-Wasserstein transport cost or as Joule heating in a resistor network.

Finally, I will share recent results, open questions, and grand ambitions regarding an extrinsic geometry of control. I will discuss how the "cost of constraint" can be framed using the second fundamental form and normal curvature, how graph automorphisms map onto manifold isometries, and highlight how geometric stability analysis (via Jacobi fields) can be used to predict when symmetry-breaking protocols become energetically optimal.