  We discuss and qualify a previously unnoticed connection between two
different phenomena in the physics of nanoscale friction, general in nature and
also met in experiments including sliding emu- lations in optical lattices, and
protein force spectroscopy. The first is thermolubricity, designating the
condition in which a dry nanosized slider can at sufficiently high temperature
and low velocity exhibit very small viscous friction f ~ v despite strong
corrugations that would commonly imply hard mechanical stick-slip f ~ log(v).
The second, apparently unrelated phenomenon present in externally forced
nanosystems, is the occurrence of negative work tails ("free lunches") in the
work probabilty distribution, tails whose presence is necessary to fulfil the
celebrated Jarzynski equality of non-equilibrium statistical mechanics. Here we
prove analytically and demonstrate numerically in the prototypical classical
overdamped one-dimensional point slider (Prandtl-Tomlinson) model that the
presence or absence of thermolubricity is exactly equivalent to satisfaction or
violation of the Jarzynski equality. The divide between the two regimes,
satisfaction of Jarzynski with ther- molubricity, and violation of both, simply
coincides with the total frictional work per cycle falling below or above kT
respectively. This concept can, with due caution, be extended to more complex
sliders, thus inviting crosscheck experiments, such as searching for free
lunches in cold ion sliding as well as in forced protein unwinding, and
alternatively checking for a thermolubric regime in dragged colloid monolayers.
As an important byproduct, we derive a parameter-free formula expressing the
linear velocity coefficient of frictional dissipated power in the thermolubric
viscous regime, correcting previous empirically parametrized expressions.
