Josephson dynamics at high transmissions: voltage and current bias limits

We establish a direct relation between the $I-V$ curves for highly transparent Josephson junctions in the voltage- and current-biased regimes. We demonstrate that the presence of sub-Ohmic dissipation at subgap voltages and temperatures yields the linear dependence of the average voltage $\overline V$ on the bias current I exceeding the critical one ${{I}_{c}}$, in contrast to the square root dependence $\overline V \propto \sqrt {I - {{I}_{c}}} $ in the Ohmic limit. Our predictions are compared with recent experimental findings.