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We study how the mass and magnetic moment of the quarks are dynamically generated in nonequilibrium quark matter. We derive the equal-time transport and constraint equations for the quark Wigner function in a magnetized quark model and solve them in the semi-classical expansion. The quark mass and magnetic moment are self-consistently coupled to the Wigner function and controlled by the kinetic equations. While the quark mass is dynamically generated at the classical level, the quark magnetic moment is a pure quantum effect, induced by the quark spin interaction with the external magnetic field.