Assimetria e produção de entropia em sistemas quânticos fora do equilíbrio: o modelo LMG sobre transições de fase quântica dinâmica

Abstract

The nonequilibrium dynamics of many-body quantum systems has attracted increasing attention due to the emergence of dynamical phenomena with no equilibrium counterpart, such as dynamical quantum phase transitions (DQPTs). In this thesis, we investigate the interplay between entropy production, symmetry, and dynamical criticality in isolated quantum systems driven far from equilibrium. We use the Lipkin–Meshkov–Glick (LMG) model as a paradigmatic platform, as it allows for an analysis of finite-size effects and symmetry sectors. Sudden quenches of the system parameters are considered, and dynamic criticality is identified through the Loschmidt echo and its associated rate function, as well as through a dynamical order parameter. Entropy production is quantified via a geometric approach based on the Bures angle, providing a lower bound to the irreversible entropy generated during the unitary dynamics, while asymmetry is characterized using measures associated with collective spin operators, enabling a dynamical analysis of this quantity during symmetry restoration induced by DQPTs. We show that the time-averaged entropy production displays clear signatures in the vicinity of the dynamical critical point, reflecting enhanced irreversibility induced by the nonequilibrium dynamics. In addition, we demonstrate that quantum asymmetry provides a robust indicator of DQPT, capturing the dynamical restoration of the underlying Z2 symmetry during the evolution. Finally, we show that the location of these signatures depend on the anisotropy parameter, highlighting its central role in dynamical critical behavior of the system.