Singular optimal driving cycles of stochastic pumps

TL;DR

This paper explores the optimal driving cycles for stochastic pumps, revealing that the most efficient cycle involves singular, infinitely rapid switching, which has implications for designing artificial molecular motors.

Contribution

It introduces a novel analysis showing that optimal thermodynamic cycles can be singular with infinite switching rates, expanding understanding of minimal dissipation processes.

Findings

Optimal cycles are singular with infinite switching rates.

Such singular solutions are common in systems with exponential relaxation.

Implications for designing efficient artificial molecular motors.

Abstract

The investigation of optimal processes has a long history in the field of thermodynamics. It is well known that finite-time processes that minimize dissipation often exhibit discontinuities. We use a combination of numerical and analytical approaches to study the driving cycle that maximizes the output in a simple model of a stochastic pump: a system driven out of equilibrium by a cyclic variation of external parameters. We find that this optimal solution is singular, with an infinite rate of switching between sets of parameters. The appearance of such singular solutions in thermodynamic processes is surprising, but we argue that such solutions are expected to be quite common in models whose dynamics exhibit exponential relaxation, as long as the driving period is not externally fixed, and is allowed to be arbitrarily short. Our results have implications to artificial molecular motors that are driven in a cyclic manner.