Quantifying and Minimizing Dissipation in a Nonequilibrium Phase Transition

In a finite-time continuous phase transition, topological defects emerge as the system undergoes spontaneous symmetry breaking. The Kibble-Zurek mechanism predicts how the defect density scales with the quench rate. During such processes, dissipation also arises as the system fails to adiabatically follow the control protocol near the critical point. Quantifying and minimizing this dissipation is fundamentally relevant to nonequilibrium thermodynamics and practically important for energy-efficient computing and devices. However, experimentally measuring dissipation, and optimizing control protocols to reduce it, remains almost completely unexplored. In addition, it is an open question to what extent dissipation is correlated with the formation of defects. Here, we directly measure the dissipation generated during the voltage-driven Fréedericksz transition of a liquid crystal with a sensitivity equivalent to a ∼10 nanokelvin temperature rise. We observe Kibble-Zurek scaling of dissipation and its breakdown, both in quantitative agreement with existing theoretical works. We further implement a fully automated in situ optimization approach that discovers more optimal driving protocols, reducing dissipation by a factor of 3 relative to a simple linear protocol.