Wasserstein speed limits for underdamped Brownian particles

We derive thermodynamic speed limits for underdamped Brownian particles subject to arbitrary forcing by utilizing the Benamou-Brenier fluid dynamics formulation of optimal mass transport. Specifically, we show that for a fixed amount of dynamical activity and entropy production, there is a fundamental limit on how fast the system can transition from an initial state ρ₀ to a final state ρ_τ. Specializing to fully reversible or fully irreversible forcing, we further derive thermodynamic bounds on the dissipation and minimum control energy required over the transition. Finally, we explore the tightness of the bounds via numerical examples. Our proposed framework can be readily extended to general Langevin systems which admit a decomposition into reversible and irreversible dynamics.