  Magnetic reconnection (MR) in collisionless plasma is often attributed to the
off-diagonal electron Reynolds stress, which can give rise to a large induction
electric field in the reconnection region. However, in magneto-hydro-dynamics
(MHD) simulations of MR, it is difficult to implement the full Reynolds stress,
which is kinetic in nature. In this paper, we propose a theoretical model of
effective resistivity from the first principle of particle dynamics. The
derived theoretical formulation of the effective resistivity is verified by
full particle-in-cell (PIC) simulations, and the corresponding physics is
discussed.
