Wasserstein speed limits for Langevin systems

TL;DR

This work extends Wasserstein-speed limits from overdamped to general Langevin systems by introducing a phase-space current decomposition into irreversible and reversible components. It proves a universal bound that couples the Wasserstein distance with the combined energetic costs Σ (entropy production) and Υ (reversible action), via τ(Σ+Φ+Υ) ≥ \\mathcal{W}_{2,\\mathbf{M}}(ρ_0,ρ_τ)^2 and related local speed bounds. The authors specialize to underdamped dynamics, derive explicit forms for Σ and Υ, and develop a coarse-graining framework that yields bounds for marginals as well as the full system; they also analyze special force-parity cases and provide two illustrative examples: a Brownian particle in a time-varying quadratic potential and a noisy RLC circuit. The results reveal that not only irreversibility but also reversible currents constrain transition speeds, offering practical insights for control and estimation in noisy nanoscale systems. Overall, the paper establishes a phase-space Wasserstein approach to universal speed limits with broad applicability to stochastic thermodynamics and controlled nonequilibrium processes.

Abstract

Physical systems transition between states with finite speed that is limited by energetic costs. In this work, we derive bounds on transition times for general Langevin systems that admit a decomposition into reversible and irreversible dynamics, in terms of the Wasserstein distance between states and the energetic costs associated with respective reversible and irreversible currents. For illustration we discuss Brownian particles subject to arbitrary forcing and an RLC circuit with time-varying inductor.

Figures (2)

• Figure 1: Lower bounds $\tau_{24}$ (dashed) and $\tau_{25}$ (dotted) on the transition time $\tau$ (solid) for different values of $\gamma/m$ using the optimal protocol in the overdamped limit.
• Figure 2: Noisy RLC Circuit with time-varying inductor.