Thermally assisted lubricity and negative work tails in sliding friction

We discuss and qualify the connection between two separate phenomena in the physics of nanoscale friction, general in nature and relevant to experiments. The first is thermally assisted lubricity (TAL), i.e., the low-velocity regime where a nanosized dry slider exhibits a viscouslike friction despite corrugations that would otherwise imply hard stick-slip friction. The second is the occurrence of negative dissipated work (NDW) events in sampling the work probability distribution. The abundance, or scarcity due to insufficient sampling, of these NDW events implies experimental fulfillment or violation of the celebrated Jarzynski equality (JE) of nonequilibrium statistical mechanics. We show, both analytically and in simulations of the one-dimensional point slider Prandtl-Tomlinson model, that a general crossover can be individuated as the total frictional work per cycle crosses kBT. Below such crossover, the TAL regime holds, the dissipation is essentially linear, and the numerical validation for the JE is feasible (i.e., does not require an exponentially large sampling size). Above it, the dissipation profile departs from linearity and gains its hard stick-slip features, and the mandatory sampling for the JE becomes exponentially large. In addition, we derive a parameter-free formula expressing the linear velocity coefficient of viscous friction, correcting previous empirically parameterized expressions. With due caution, the connection between friction and work tails can be extended beyond a single degree of freedom to more complex sliders, thus inviting realistic crosscheck experiments. Of importance for experimental nanofriction will be the search for NDW tails in the sliding behavior of trapped cold ions, and alternatively checking for TAL in the sliding pattern of dragged colloid monolayers as well as in forced protein unwinding.