Ratchet-induced variations in bulk states of an active ideal gas

TL;DR

This paper investigates how a ratchet potential influences the distribution of active particles in two bulk states, revealing long-range effects and challenging the effective temperature concept through analytical and transition state models.

Contribution

It provides an analytical solution showing long-range influence of ratchet potentials on active particles and introduces a transition state model to explain the observed power law dependencies.

Findings

Ratchet potential affects particle distribution over long distances.

Power law dependencies of bulk density differences on system parameters.

Effective temperature concept does not hold in this active system.

Abstract

We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks, and thus exerts an influence of infinitely long range. As we show, crucial for having such a long-range influence is an external potential that is nonlinear. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameters in several limiting cases. While weakly active systems are often understood in terms of an effective temperature, we present an analytical solution that explicitly shows that this is not possible in the current setting. Instead, we rationalize our results by a simple transition state model, that presumes particles to cross the potential barrier by Arrhenius rates modified for activity. While this model does not quantitatively describe the difference in bulk densities for feasible parameter values, it does reproduce - in its regime of applicability - the complete power law behavior correctly.