In this paper, entropy generation of associated with double diffusive natural convection of non Newtonian power-law fluids in an open cavity in the presence of a horizontal magnetic field, studying Soret and Dufour parameters has been analyzed by FDLBM (Finite Difference Lattice Boltzmann method). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10(4) and 10(5)), Hartmann number (Ha = 0, 15, and 30), power-law index (n = 0.6, 1, and 1.4), Lewis number (Le = 2.5 and 5), Dufour parameter (D-f = 0, 1, and 5), Soret parameter (S-r = 0,1, and 5) and the buoyancy ratio (N = -1 and 1). Results indicate that the augmentation of the thermal Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Hartmann number provokes various irreversibilities to enhance and the average Bejan number decreases significantly. The enhancement of Lewis number and buoyancy ratio affect various entropy generations and the average Bejan number. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The change of power-law index alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters. (C) 2016 Elsevier Ltd. All rights reserved.