The friction coefficient
of fluids may become a function of the
velocity at increased external driving. This non-Newtonian behavior
is of general theoretical interest and of great practical importance,
for example, for the design of lubricants. Although the effect has
been observed in large-scale atomistic simulations of bulk liquids,
its theoretical formulation and microscopic origin are not well understood.
Here, we use dissipation-corrected targeted molecular dynamics, which
pulls apart two tagged liquid molecules in the presence of surrounding
molecules, and analyze this nonequilibrium process via a generalized
Langevin equation. The approach is based on a second-order cumulant
expansion of Jarzynski’s identity, which is shown to be valid
for fluids and therefore allows for an exact computation of the friction
profile as well of the underlying memory kernel. We show that velocity-dependent
friction in fluids results from an intricate interplay of near-order
structural effects and the non-Markovian behavior of the friction
memory kernel. For complex fluids such as the model lubricant C40H82, the memory kernel exhibits a stretched-exponential
long-time decay, which reflects the multitude of timescales of the
system.