To explain the strange behavior of superfluid helium at low temperatures, Landau proposed the two-fluid model that incorporates quantum mechanics. In this model the liquid is split into a viscous “normal” component and a zero-viscosity “superfluid” component, each flowing independently. He also showed that excitations in the superfluid come in two kinds, phonons and rotons, and from their energy spectrum he derived the critical velocity and heat-transport properties. His theory agreed remarkably well with experimental data and became the standard framework of low-temperature physics. The friction-free nature of superfluids is now used in ultra-sensitive gyroscopes and designs for loss-free piping. Landau’s work also helped organize condensed-matter physics as a coherent discipline.

When deriving the equations of motion for superfluid helium-II, Landau introduced a single dispersion relation ε(p)=cp+Δ+(p−p0)^2/2μ that unifies the phonon regime and the roton minimum. From this relation he obtained the Landau critical velocity v_c=min[ε(p)/p], the maximum speed the liquid can reach without becoming turbulent, which matches experiments. His two-fluid thermodynamics accurately predicted quantities such as specific heat and the velocity of second sound. He also applied Fermi-liquid theory to 3He, analyzing its paramagnetism, effective mass, and quasiparticle interactions to explain the anomalous low-temperature heat capacity. These theories supplied condensed-matter physics with core concepts like quasiparticles, diagonalization techniques, and the adiabatic approximation. Landau’s ideas still influence magnetotransport studies and the physics of Bose–Einstein condensates in neutral atomic gases.

For liquid 4He, Landau posited an excitation spectrum with distinct phonon and roton branches and formulated two-fluid hydrodynamics using ρ_s and ρ_n. Coupled equations for a viscous normal component obeying Navier–Stokes dynamics and an inviscid superfluid component with quantized circulation κ=h/m yield second-sound propagation and thermal counter-flow. The roton gap Δ contributes to the Pomeranchuk effect and the melting line of 3He–4He mixtures, consistent with pressure-dependent critical parameters observed experimentally. In Fermi-liquid theory he introduced the effective mass m* and Landau parameters F_l^s,a, reproducing the low-temperature specific heat C_V=π^2k_B^2N(0)T/3·(m*/m). Scaling theory for quantum many-body systems and Ginzburg–Landau relations for phase transitions connect directly to Landau’s framework, offering prototypes for flux–force relations in non-equilibrium thermodynamics.