We present the results of our quasi-simultaneous radio, sub-mm, infrared, optical and X-ray study of the Galactic black hole candidate X-ray binary MAXI J1836-194 during its 2011 outburst. We consider the full multi-wavelength spectral evolution of the outburst, investigating whether the evolution of the jet spectral break (the transition between optically-thick and optically-thin synchrotron emission) is caused by any specific properties of the accretion flow. Our observations show that the break does not scale with the X-ray luminosity or with the inner radius of the accretion disk, and is instead likely to be set by much more complex processes. We find that the radius of the acceleration zone at the base of the jet decreases from ~10$^6$ gravitational radii during the hard intermediate state to ~10$^3$ gravitational radii as the outburst fades (assuming a black hole mass of 8 M$_{odot}$), demonstrating that the electrons are accelerated on much larger scales than the radius of the inner accretion disk and that the jet properties change significantly during outburst. From our broadband modelling and high-resolution optical spectra, we argue that early in the outburst, the high-energy synchrotron cooling break was located in the optical band, between $approx 3.2 times 10^{14}$ Hz and $4.5 times 10^{14}$ Hz. We calculate that the jet has a total radiative power of $approx 3.1 times 10^{36}$ ergs s$^{-1}$, which is ~6% of the bolometric radiative luminosity at this time. We discuss how this cooling break may evolve during the outburst, and how that evolution dictates the total jet radiative power. Assuming the source is a stellar-mass black hole with canonical state transitions, from the measured flux and peak temperature of the disk component we constrain the source distance to be 4-10 kpc.
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