Convert thermal conductivity from Lennard-Jones (reduced units) to SI

Hi dear users,

I am running a simulation using Lennard Jones units and I am calculating the thermal conductivity of some materials. How would I go about converting it from reduced units to SI units?

Thanks in advance for any help

See a textbook on reduced units, e.g. Allen & Tildesley, and how
they are unitless. Start with something simple like temperature
and figure out how to use a fomula like T* = kb T / epsilon to
map back to real units. Kappa will be more complicated, i.e. you
need to derive the equivalent formula that contains both Kappa* and Kappa.