Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum phase transition (QPT). In this paper, we illustrate that the system dynamics can be elucidated by considering the precession of a collection of free pseudospins under a magnetic field based on the exact results of extended Kitaev chains. The topology of the driven Hamiltonian is determined by the average winding number of the nonequilibrium state. Furthermore, we establish that the singularity of the DQPT arises from two perpendicular pseudospin vectors associated with the pre- and postquenched Hamiltonians. Moreover, we investigate the distinct behaviors of the dynamic pairing order parameter in both topological and nontopological regions. These findings offer valuable insights into the non-equilibrium behavior of topological superconductors, contributing to the understanding of the resilience of topological properties in driven quantum systems.

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• Dynamical phase transitions
• Magnetization dynamics
• Quantum phase transitions
• Quantum quench
• Nonequilibrium systems
• Quantum many-body systems
• Topological superconductors
• Dynamic critical phenomena
• Exact solutions for many-body systems
• Nuclear magnetic resonance