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Taking inspiration from F. Bloch’s seminal work (PRA 7, 2187 (1973)), we investigate the quantum many-body states of superfluid ⁴He, unveiling a novel characteristic in the system’s energy levels. Below the transition temperature, the thermally active low-energy levels exhibit a distinctive grouping behavior, with each level belonging exclusively to a single group. In a superflow state, the system establishes thermal equilibrium with its surroundings on a group-specific basis. Specifically, the levels within a chosen group, initially populated, undergo thermal redistribution, while the remaining groups of levels stay vacant due to absence of transitions between groups. The macroscopic properties of the system, such as its superflow velocity and thermal energy density, are statistically determined by the thermal distribution of the occupied group. Additionally, we infer that the thermal energy of a superflow has an unusual relationship with flow velocity, such that the larger the flow velocity, the smaller the thermal energy. This relationship is responsible for a range of intriguing phenomena, including the mechano-caloric effect and the fountain effect, which demonstrate a fundamental coupling between the thermal motion and hydrodynamic motion of the system. Furthermore, we present experimental evidence of a self-heating effect in ⁴He superflows, confirming that a ⁴He superflow carries significant thermal energy related to its velocity.

We obtain the possible transport in an annulus filled with solid helium of which parts are of supersolidity near the interface. Our transport results qualitatively resemble those recently reported measurements.

We review on a recently proposed quantum exception to the second law of thermodynamics (SLT). We emphasize that ⁴He superflows, like any other forms of flows, shall carry entropy or heat in a thermal environment. Following that, one can use a heterogeneous ⁴He superflow loop to realize entropy-decreasing processes. We also mention that the heat content of a superflow has an unusual dependence on flow velocity, which is an important factor contributing to the entropy-decreasing processes.