Finite-frequency extension of stochastic scallop propulsion

Extend the slow-driving geometric framework for stochastic scallop propulsion to finite driving frequencies, determine the higher-order corrections to the probability distribution, pumped displacement, and entropy production, and establish whether a useful generalization of the thermodynamic-length description survives beyond the adiabatic regime.

Background

The paper derives the Berry–Sinitsyn–Nemenan (BSN) geometric displacement and the thermodynamic metric within a slow-driving expansion characterized by a small parameter. This approximation captures the quasistatic geometric contribution to propulsion and the leading non-adiabatic correction to entropy production.

The authors explicitly note that higher driving frequencies may make higher-order corrections important. They leave unresolved how geometric pumping and thermodynamic dissipation are modified at finite frequency and whether the thermodynamic-length formulation remains useful outside the adiabatic regime.