During discharges of an arc plasma, complex mass, momentum and energy exchanges exist between the arc column and the surrounding cold gas, forming a nonequilibrium region deviating from both the local thermodynamic equilibrium and local chemical equilibrium states. The nonequilibrium synergistic transport plays a crucial role not only in controlling the characteristics of the arc plasmas theoretically, but also in optimizing the plasma material processing qualities in actual applications. In this paper, the nonequilibrium transport processes in free-burning argon arc plasmas under different operating pressures and arc currents are studied based on a complete nonequilibrium fluid model, and are also validated by comparing with measured data. The energy transfer processes under various operating conditions, especially Joule heating, elastic and inelastic collisions, conductive and convective heat transfer, and energy transfer related to the temperature ratio spatial gradient, are analyzed based on the concept of the ‘energy tree.’ The revealed major energy transfer channels in the high-pressure argon arc plasmas also provide some possibilities to control the characteristics of thermal plasmas in the future.