Modeling the effects of perturbations and steepest entropy ascent on the time evolution of entanglement

This work presents an analysis of the evolution of perturbed Bell diagonal states using the equation of motion of steepest-entropy-ascent quantum thermodynamics (SEAQT), the Lindblad equation, and various measures of entanglement loss. The Bell diagonal states considered are those generated by the quantum optics study conducted by Liu et al (2016 Phys. Rev. A 94 062107). First, a brief derivation is provided, showing that Bell diagonal states are stationary but not stable equilibrium states within the SEAQT formalism. This highlights the need for perturbation methods to study the evolution of nearby states with, for example, similar values of the energy and entropy. In contrast, under the Lindblad equation of motion, only some Bell diagonal states remain stationary. Although SEAQT is a non-standard, nonlinear framework, it exhibits several unique features that other approaches do not. In particular, not only does it satisfy the postulates of quantum mechanics, but it, as well, is fully compatible with the second law of thermodynamics, providing a physically consistent description of non-equilibrium quantum systems. The perturbation methods used include a weighted-average method for perturbing bipartite system states and a general bipartite method based on a set of unitary operations constrained to maintain constant system energy and entropy. Sets of density operators are randomly generated using each method, and the resulting time-dependent characteristics of the entanglement are analyzed within the SEAQT and Lindblad frameworks. The findings reveal that the evolutions associated with constrained perturbations accurately predict the loss of non-locality and align well with measured concurrence. Additionally, within the SEAQT framework, the deep connection between the thermodynamic states of the evolution of the system and the loss of non-locality is quantitatively demonstrated.