  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.
