Violation of thermodynamic speed limits as a criterion for physical model selection

Abstract Machine learning algorithms are now being used to automate the discovery of physical equations from measurement data. However, under or overfitting the dynamics can lead to model misspecification and unreliable predictions. Here we show that thermodynamic speed limits–fundamental bounds on the rates of heat, entropy, and other observables–provide a diagnostic: if essential dynamics are omitted, observable speeds can appear to exceed the bound. These apparent violations signal missing physics and a structurally incomplete description of the dynamics. Using an underdamped Langevin oscillator and an active Brownian particle as benchmarks, we prove that neglecting inertia or activity leads to observable rates that exceed the limit, in some cases indefinitely. Because true violations are impossible, speed-limit violations are a criterion for rejecting physically inconsistent representations of nonequilibrium processes.