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Recently, particle in cell (PIC) simulations have shown that relativisticturbulence in collisionless plasmas can result in an equilibrium particledistribution function where turbulent heating is balanced by radiative coolingof electrons. Strongly magnetized plasmas are characterized by higher energypeaks and broader particle distributions. In relativistically movingastrophysical jets, it is believed that the flow is launched Poynting fluxdominated and that the resulting magnetic instabilities may create a turbulentenvironment inside the jet, i.e., the regime of relativistic turbulence. Inthis paper, we extend previous PIC simulation results to larger values ofplasma magnetization by linearly extrapolating the diffusion and advectioncoefficients relevant for the turbulent plasmas under consideration. We usethese results to build a single zone turbulent jet model that is based on theglobal parameters of blazar emission region, and consistently calculate theparticle distribution and resulting synchrotron and inverse Compton emissionspectra. We then test our model by comparing its predictions with thebroad-band quiescent emission spectra of a dozen blazars. Our results show goodagreement with observations of low-synchrotron peaked (LSP) sources and findthat LSPs are moderately Poynting flux dominated with magnetization $1\lesssim\sigma \lesssim 5$, have bulk Lorentz factor $\Gamma\sim 10-30$, and that theturbulent region is located at the edge, or just beyond, the broad line region(BLR). The turbulence is found to be driven at an area comparable to the jetcross section.

Balancing Turbulent Heating with Radiative Cooling in Blazars