Optical modes possessing orbital angular momentum constitute a very useful platform for experimental studies on the quantum limits of thermodynamics. Here, we present experimental results for entangled photon pairs subjected to thin turbulence simulated with spatial light modulators and interpret them in the context of the generalized Jarzynski's fluctuation relation. By holographic measurement of the orbital angular momentum, we obtain the work distribution produced by the turbulence for single- and double-sided turbulence channels. The use of Klyshko's advanced-wave picture allows us to interpret the experimental scheme as a two-way process in a fully quantum picture.