General no-go condition for stochastic pumping

TL;DR

This paper establishes fundamental limitations on stochastic pumping in chemical systems, extending previous no-go theorems to non-Markovian dynamics and showing how certain protocols cannot generate net currents.

Contribution

It provides simplified proofs of no-go theorems for stochastic pumping, including extensions to non-Markovian dynamics and the diffusion limit, clarifying constraints on molecular motor protocols.

Findings

Certain protocols changing only energy well depth cannot produce net currents.

Pre-existing steady state currents are scaled by a factor under time-dependent modulation.

The results extend no-go theorems to non-Markovian and diffusion limit regimes.

Abstract

The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemo-mechanical molecular configurations. Pumping refers to generating a net current, e.g. per period in the time-dependence, through a cycle of consecutive states. The working of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are in general modified with a multiplicative factor when this time-dependence is turned on.