The main objective of this paper is to study the phase transition of the liquid 4He system with non-homogenous density, which is an extension of the work in Yang and Zhang, Discrete Cont. Dyn.-B, 24, 5107–5120 (2019). Based on the new Gibbs free energy and the unified mathematical model for the statistical physics proposed by Ma and Wang, we derive the general dynamic model of the liquid 4He system with non-homogenous density. By using the dynamical phase transition theory, the superfluidity transition occurs for the liquid 4He system, when parameters go through the critical condition depending on the scale of occupying domain.
Zhou et al. (Sun,) studied this question.