Dynamical quantum phase transitions and quantum thermodynamics: An approach through dynamical transformations

Quantum mechanics provides various pictures for understanding physical phenomena, yet the full potential of these pictures' equivalence remains underutilized. This work introduces a novel picture, opposite to the interaction picture, achieved through a transformation of the time evolution operator. This new approach permits the manipulation of the relative weight of Hamiltonian components. Utilizing picture equivalence, we investigate dynamical quantum phase transitions and quantum thermodynamics. Our findings reveal a significant relationship between dynamical topological quantum phase transitions and accidental ones through time-reversal operations, offering new insights into their fundamental connections. Moreover, our picture-based transformation addresses the challenge of defining thermodynamic quantities in systems with strong system-reservoir coupling, maintaining the robustness of weak coupling analyses.