Benchmarking heat engines for Reissner-Nordström black holes in Rényi statistics

We construct benchmarking heat engines for asymptotically flat Reissner–Nordström black holes within an effective Rényi extended phase-space description. The Rényi non-extensivity parameter induces an effective pressure, allowing a pressure–volume sector to be introduced without a cosmological constant. At fixed electric charge, the heat flow is evaluated from the adopted first-law prescription, [Formula: see text], while [Formula: see text] is reconstructed along the cycle from the equation of state. For elliptic benchmarking cycles, the efficiency increases with the cycle size, the charge, and the central Rényi parameter [Formula: see text] over the parameter ranges considered. The numerical heat balance provides a stringent check of the integration procedure, and the resulting efficiencies remain below the comparative Carnot-type upper bound defined by the maximum and minimum temperatures reached along the cycle. A matched-pressure comparison with the standard RN-AdS engine further shows that statistical and geometric pressure sectors can lead to different heat-engine responses.