A Lindblad model for a spin chain coupled to heat baths

We study a XY model which consists of a spin chain coupled to heat baths. We give a repeated quantum interaction Hamiltonian describing this model. We compute the explicit form of the associated Lindblad generator in the case of the spin chain coupled to one, two and several heat baths. We further study the properties of quantum master equation such as approach to equilibrium, local equilibrium states, entropy production and quantum detailed balance condition.