Accurate and useful analytic approximations are developed for order parameter profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates. The pure condensates 1 and 2, each of which contains a particular species of atoms, feature healing lengths ξ 1 and ξ 2 . The inter-atomic interactions are repulsive. In particular, the effective inter-species repulsive interaction strength is K. A triple-parabola approximation (TPA) is proposed, to represent closely the energy density featured in Gross-Pitaevskii (GP) theory. This TPA allows us to define a model, which is a handy alternative to the full GP theory, while still possessing a simple analytic solution. The TPA offers a significant improvement over the recently introduced double-parabola approximation (DPA). In particular, a more accurate amplitude for the wall energy (of a single condensate) is derived and, importantly, a more correct expression for the interfacial tension (of two condensates) is obtained, which describes better its dependence on K in the strong segregation regime, while also the interface profiles undergo a qualitative improvement.

The n-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.