  Characterizing the thermodynamics of turbulent plasmas is key to decoding
observable signatures from astrophysical systems. In magnetohydrodynamic (MHD)
turbulence, nonlinear interactions between counter-propagating Alfv\'en waves
cascade energy to smaller spatial scales where dissipation heats the protons
and electrons. When the thermal pressure far exceeds the magnetic pressure,
linear theory predicts a spectral gap at perpendicular scales near the proton
gyroradius where Alfv\'en waves become non-propagating. For simple models of an
MHD turbulent cascade that assume only local nonlinear interactions, the
cascade halts at this gap, preventing energy from reaching smaller scales where
electron dissipation dominates, leading to an overestimate of the proton
heating rate. In this work, we demonstrate that nonlocal contributions to the
cascade, specifically large scale shearing and small scale diffusion, can
bridge the non-propagating gap, allowing the cascade to continue to smaller
scales. We provide an updated functional form for the proton-to-electron
heating ratio accounting for this nonlocal energy transfer by evaluating a
nonlocal weakened cascade model over a range of temperature and pressure
ratios. In plasmas where the thermal pressure dominates the magnetic pressure,
we observe that the proton heating is moderated compared to the significant
enhancement predicted by local models.
