Information Entropy for a Two-Dimensional Rotating Bose–Einstein Condensate

We study the information entropy, order, disorder, and complexity for the two-dimensional (2D) rotating and nonrotating Bose–Einstein condensates. The choice of our system is a complete theoretical laboratory where the complexity is controlled by the two-body contact interaction strength and the rotation frequency (\(\varOmega \)) of the harmonic trap. The 2D nonrotating condensate shows the complexity of the category I where the disorder-order transition is triggered by the interaction strength. In the rotating condensates, \(\varOmega \) is chosen as the disorder parameter when the interaction strength is fixed. With respect to \(\varOmega \), the complexity shifts between maximum and minimum confirm the existence of category II complexity in the rotating condensate. Also, we consider the interaction strength as the disorder parameter when \(\varOmega \) is unchanged and complexity as a function of interaction strength exhibits category III complexity. The present work also includes the calculation of upper bound and lower bound of entropy for 2D quantum systems.