  The pulsar wind nebula associated with PSR J1826-1334, HESS J1825-137, is a
bright very high energy source with an angular extent of ~1 degree and
spatially-resolved spectroscopic TeV measurements. The gamma-ray spectral index
is observed to soften with increasing distance from the pulsar, likely the
result of cooling losses as electrons traverse the nebula. We describe analysis
of X-ray data of the extended nebula, as well as 3-D time-dependent spectral
energy distribution modeling, with emphasis on the spatial variations within
HESS J1825-137. The multi-wavelength data places significant constraints on
electron injection, transport, and cooling within the nebula. The large size
and high nebular energy budget imply a relatively rapid initial pulsar spin
period of 13 \pm 7 ms and an age of 40 \pm 9 kyr. The relative fluxes of each
VHE zone can be explained by advective particle transport with a radially
decreasing velocity profile with $v(r) \propto r^{-0.5}$. The evolution of the
cooling break requires an evolving magnetic field which also decreases radially
from the pulsar, $B(r,t) \propto r^{-0.7} \dot{E}(t)^{1/2}$. Detection of 10
TeV flux ~80 pc from the pulsar requires rapid diffusion of high energy
particles with $\tau_{esc} \approx 90 (R / 10 pc)^2 (E_e/100 TeV)^{-1}$ year,
contrary to the common assumption of toroidal magnetic fields with strong
magnetic confinement. The model predicts a rather uniform Fermi LAT surface
brightness out to ~1 degree from the pulsar, in good agreement with the
recently discovered LAT source centered 0.5 degree southwest of PSR J1826-1334
with extension 0.6 \pm 0.1 degree.
