Information-theoretic measures and thermodynamic properties under magnetic and Aharonov–Bohm flux fields

We investigated the effects of external magnetic and Aharonov–Bohm flux fields on the thermodynamic properties, Fisher, Shannon and Rényi information-theoretic measures using the non-relativistic Schrödinger equation with a Varshni-type potential. We adopted the parametric Nikiforov–Uvarov approach to obtain the analytical bound states in closed form. The thermodynamic functions such as the free energy, specific heat capacity, vibrational entropy and mean energy were analyzed. Also, the results for the 2D Fisher's information-theoretic measure obey the inequality $$I\left(\rho \right)I\left(\gamma \right)\ge 16$$ . The Rényi entropies sum applied to lithium hydride (LiH) diatomic molecule obeys the inequality $${R}_{2}\left(\rho \right)$$ + $${R}_{2/3}\left(\gamma \right)\ge $$ 4.19926 for 2D system. Also, the global Shannon entropies sum inequality for the LiH molecule is verified. The applications of the external fields were found to strongly influence the splitting of the energy overlaps, the thermodynamic functions and the information-theoretic measures. The results may aid the understanding of the dynamics of quantum particles and molecules in external fields.