We present new data on the nonequilibrium acoustic response of glasses to an applied dc electric field below 1K. When compared with the analogous dielectric response of the same material, the acoustic data show, within experimental precision, identical dependence on the perturbing field, but stronger temperature dependence. These data are difficult to reconcile with simple generalizations of the dipole gap model of two-level system (TLS) dielectric response, unless we assume that as T is decreased, interaction-based TLS collective effects increase.The equilibrium thermodynamic, acoustic, and dielectric properties of amorphous materials at low temperatures are described well by the tunneling two-level system (TLS) model [1]. Given a large number of independent TLS with a broad distribution of energy asymmetries ∆ and tunneling parameters ∆ 0 (P (∆, ∆ 0 ) = P 0 /∆ 0 , where P 0 is a contant), the model predicts a specific heat C ∼ T and a thermal conductivity κ ∼ T 2 , in fair agreement with the universal behavior noted by Zeller and Pohl [2]. TLS reach thermal equilibrium with the phonon bath by coupling to local strain fields u, which shift asymmetries by γ · u, where γ ≈ 1 eV. Via this coupling, the TLS contribute to the equilibrium sound speed and internal friction [3]. If the TLS have intrinsic electric dipole moments of magnitude p, the TLS contribution to the equilibrium dielectric response [4] is strictly analogous.The equilibrium sound speed v has a maximum at a temperature T m ≈ 50 mK. For T > T m , the "relaxational regime", TLS behavior is dominated by single-phonon relaxational processes, while for T < T m , the "resonant regime", resonant quantum tunneling of the TLS dominates their response to an ac strain field. The real part of the dielectric response ǫ ′ behaves analogously, but with an overall sign difference. In both v and ǫ ′ the crossover temperature T m at measuring frequency ω is set by the TLS-phonon coupling, T m = ω A 1 3 , where A ∝ γ 2 . Recent measurements [5][6][7] of the nonequilibrium dielectric response of glasses are consistent with a model [14] in which weak dipolar TLS-TLS interactions produce a "dipole gap" in the TLS density of states near zero local electric and strain fields. The gap is necessary to ensure the stability of the ground state, and has been discussed elsewhere [16] in connection with spin glasses.We concentrate on "sweep" experiments, in which an applied electric field, E dc , is slowly varied in time as a triangle wave, and the nonequilibrium dielectric response is measured as a function of that field. This response shows a minimum at zero applied bias (a "zero bias hole"), which becomes sharper and deeper as the temperature is lowered. These sweep data are interpreted as an observation of the proposed gap in the TLS density of states. While the external field is swept, TLS with short relaxation times compared to the period of the sweep partly fill the zero bias hole, an effect which is most important when T < ∼ 15 mK. Slower TLS continue to exhibit a depresse...