expansion is only valid in the low load regime. For averaged values of all aperiodic paths the relative error reaches $10\%$ at a load of $\unit[90]{pN}$ which corresponds to a pressure of and should be regarded as the uttermost limit for the Taylor expansion. This low load regime is discussed in more detail later in the paper.

While all quasi aperiodic paths investigated for sufficiently long paths converge to the same friction force, there is a clear difference with respect to periodic ones, see Figs. \[fig:4\] and \[fig:5\]. As expected the $30^\circ$ path exhibits the largest friction as for each period it traverses the global maximum of the unrelaxed energy surface created by the on-top position of the contact atoms. This is in contrast to the $0^\circ$ path, which shows the least friction force at zero load and also the slowest increase with rising load.

As the energy loss for the $0^\circ$ path at zero load is underestimated by about 25% within our model compared to the shearing calculations, the difference between the aperiodic and the $0^\circ$ paths might actually be smaller than predicted. However, even if $F_0(0^\circ)$ is underestimated by our approach, in case that this discrepancy stays approximately 