In the LB literature, the force-free form of the Boltzmann equation is used for the sake of simplicity. What's the rule of an external force? While for the change of the distribution function of a particle from f(r,c,t) to f(r+cdt,c+Fdt,t+dt) an external force F is applied to the particle, the Boltzmann equation is simplified as df/dt+c.div(f)=Q for system without an external force. Are those forces conceptually different?

Thanks in advance.