What is the basis for the kinematic relation between the plastic velocity gradient and slip rate in crystal plasticity framework

One of the fundamental kinematic equation in crystal plasticity is the relation between the velocity gradient and slip rate.

[ Please find the equation in the attached figure ]

In general terms, L is the spatial velocity gradient ( partial _v / partial_x )  which is a continuum quantity
 
Lp is a portion of L

Now, the RHS of the equation - gamma_dot, s and m are the slip level quantities essentially at the length scale of lattice

Questions :

1) What does the right hand side physically mean ( the product of slip rate and schmid tensor )  and how is it equivalent to the plastic velocity gradient

2) We are equating a continuum level quantity to something at a length scale of lattice, Can we do that ?

Thanks,

Prithivi