Plasma shocks are very common occurrences, and diffusive shock acceleration is a simple and efficient mechanism for generating cosmic rays. A shock's main effect is turbulent dissipation, which rapidly thermalizes the downstream plasma. Diffusive shock acceleration produces a non-thermal component to the particle distributions (quasi-power-law tails) which translates to non-thermal photon spectra, as seen in supernova remnants, jets in active galactic nuclei, and gamma-ray bursts. In supernova remnants, X-ray observations show that inferred proton temperatures are considerably cooler than standard shock heating predicts. A cross-shock electrostatic potential, akin to a double layer, is reasoned to exist in certain conditions due to the different inertial gyration scales of the plasma species. It provides a mechanism for energy exchange between species, and should result in a respective heating/cooling of the electrons/ions. It modifies the electron/ion distributions, which couple through radiative processes to the observed X-ray emission. In this thesis, the effects of cross-shock electrostatics are explored using a Monte Carlo simulation, where test particles gyrate and stochastically diffuse in a background fluid pre-defined by MHD jump conditions.A cross-shock electric field is derived from the steady-state spatial distribution of particles via a modified Poisson's equation that includes Debye screening, and the simulation is rerun with this field superimposed on the background magnetic and drift electric fields. This feedback loop continues until a self-consistent solution is obtained. Results show a significant departure of the particle distributions from the usual thermal+power-law form, and clearly demonstrates substantial energy exchange between the electron and ion populations.