In previous papers (e.g. physics/0003080 and references therein), it was pointed out that Lorentz symmetry violation (LSV) at Planck scale can play a crucial role in astrophysical processes at very high energy. It can potentially inhibit radiation under external forces (e.g. synchrotron-like), GZK-like cutoffs, decays, photodisintegration of nuclei, momentum loss trough collisions (e.g. with a photon wind in reverse shocks), production of lower-energy secondaries&ellip; . An updated description of this phenomenon is presented, focusing on acceleration in relativistic shocks and having in mind a model where the effective parameter driving LSV would vary like the square of the momentum scale (Quadratically Deformed Relativistic Kinematics, QDRK). Implications for ultra-high energy (UHE) neutrino production are equally discussed. ©2001 American Institute of Physics.