  We consider a quantum point contact between two Luttinger liquids coupled to
a mechanical system (oscillator). For non-vanishing bias, we find an effective
oscillator temperature that depends on the Luttinger parameter. A generalized
fluctuation-dissipation relation connects the decoherence and dissipation of
the oscillator to the current-voltage characteristics of the device. Via a
spectral representation, this result is generalized to arbitrary leads in a
weak tunneling regime.
