  Non-equilibrium molecular dynamics simulations, of crucial importance in
sliding friction, are hampered by arbitrariness and uncertainties in the way
Joule heat is removed. We implement in a realistic frictional simulation a
parameter-free, non-markovian, stochastic dynamics, which, as expected from
theory, absorbs Joule heat precisely as a semi-infinite harmonic substrate
would. Simulating stick-slip friction of a slider over a 2D Lennard-Jones
solid, we compare our virtually exact frictional results with approximate ones
from commonly adopted empirical dissipation schemes. While the latter are
generally in serious error, we show that the exact results can be closely
reproduced by a viscous Langevin dissipation at the boundary layer, once the
back-reflected frictional energy is variationally optimized.
