Quantum dynamical criticality speeds up thermodynamic entropy production

The thermodynamics of quantum phase transitions has long been a rich area of research, providing numerous insights and enhancing our understanding of this important phenomenon. This theoretical framework has been well-developed specially because quantum phase transitions occur at equilibrium. However, its dynamical counterpart, known as dynamical quantum phase transitions (DQPTs), takes place out-of-equilibrium, where conventional thermodynamic tools are inapplicable. In this work, we make progress in this area by connecting dynamical criticality to the second law of thermodynamics through a geometric perspective on entropy production. Our findings, along with other recent developments, suggest that dynamical criticality can lead the system to highly complex dynamics, indicating a possible pathway to thermalization.