arXiv:2511.22424v2 Announce Type: replace Abstract: Implicit discretizations of parabolic partial differential equations with hysteresis pose significant challenges for the design of robust nonlinear solvers due to the underlying history dependence. In this work, we derive a unified abstract formulation for the resulting nonlinear systems and show that their nonlinearities possess a monotone piecewise smooth structure with evolving switching behavior. Motivated by this structure, we develop a smoothing Newton method based on structure-preserving smoothing criteria, combining monotonicity preservation with an intermediate slope property. Under these conditions, the proposed method is shown to be globally convergent and locally Q-quadratically convergent. To enable practical implementation, we further introduce an explicit arc-based smoothing construction, thereby bridging the gap between abstract convergence theory and implementable algorithms. Numerical experiments for transient eddy-current problems with Preisach hysteresis demonstrate the robustness and efficiency of the proposed method compared with existing approaches.