Title: Microscopic picture of superfluid $^4$He

Abstract: We illustrate the microscopic quantum picture of superfluid helium-4 with the help of revealing a hidden property of its many-body levels. We show that, below the transition point, the low-lying levels of the system form a grouping structure with each level belonging to one specific group only. In a superflow state or a static state, the system establishes a group-specific thermal equilibrium with its environment and the levels of an initially-occupied group shall be thermally distributed. The other initially-unoccupied groups of levels remain unoccupied, due to the fact that inter-group transitions are prohibited. The macroscopically observable physical quantities of the system, such as superflow velocity and thermal energy density, are determined statistically by the thermal distribution of the occupied group(s). We further show that thermal energy of a superflow has an unusual flow velocity dependence: the larger the velocity is, the smaller the thermal energy. This velocity dependence is responsible for several intriguing phenomena of the system, such as the mechano-caloric effect and the fountain effect, which demonstrate a fundamental coupling between the thermal motion of the system and its hydrodynamic motion. We report an experimental observation of a counter-intuitive self-heating effect of $^4$He superflows, which confirms that a helium-4 superflow carries significant thermal energy depending on its velocity.