Necessity of memory for directed transport

Determine whether the presence of memory is necessary for directed motion to occur in non-Markovian Brownian systems.

Background

The dissertation demonstrates that short memory can reverse the direction of Brownian-particle transport in periodic potentials, including memory-induced absolute negative mobility and memory-induced current reversal. These results establish that memory can strongly influence transport, but they do not determine whether memory is indispensable for generating directed motion in some systems.

The authors leave unresolved the broader relationship between temporal correlations and the emergence of directed transport, specifically whether directed motion can require memory rather than merely being modified by it.