The efficiency of particle acceleration at shock waves in relativistic,
magnetized astrophysical outflows is a debated topic with far-reaching
implications. Here, for the first time, we study the impact of turbulence in
the pre-shock plasma. Our simulations demonstrate that, for a mildly
relativistic, magnetized pair shock (Lorentz factor Ξ³shββ2.7, magnetization level Οβ0.01), strong turbulence can revive
particle acceleration in a superluminal configuration that otherwise prohibits
it. Depending on the initial plasma temperature and magnetization,
stochastic-shock-drift or diffusive-type acceleration governs particle
energization, producing powerlaw spectra dN/dΞ³βΞ³βs with sβΌ2.5β3.5. At larger magnetization levels, stochastic
acceleration within the pre-shock turbulence becomes competitive and can even
take over shock acceleration