  We study the out-of-equilibrium transport in a Tomonaga-Luttinger liquid
containing a weak or a tunneling barrier coupled to an arbitrary
electromagnetic environment. This applies as well to a coherent one-channel
non-interacting conductor with a transmission coefficient close to one or to
zero. We derive formal expressions for the current and finite-frequency (FF)
noise at arbitrary voltages, temperatures and frequency-dependent impedance
$Z(\omega)$ in the regimes of weak and strong backscattering. We show that
these two regimes are no longer related by duality at finite frequency. We then
carry explicit computations of the nonlinear conductance and FF noise when
$Z(\omega)$ describes an harmonic oscillator such as a LC circuit or a cavity.
