Bacterial efflux pumps that transport antibacterial drugs out of the bacterial cells have broad specificity, commonly leading to broad spectrum resistance and limiting treatment strategies for infections. It remains unclear how efflux pumps can maintain this broad spectrum specificity to diverse drug molecules while limiting the efflux of other cytoplasmic content. We investigate the origins of this broad specificity using theoretical models informed by the experimentally determined structural and kinetic properties of efflux pumps. We develop a set of mathematical models describing operation of efflux pumps as a discrete cyclic stochastic process across a network of states characterizing pump conformations and the presence/absence of bound ligands and protons. We find that the pump specificity is determined not solely by the drug affinity to the pump–as is commonly assumed–but it is also directly affected by the periplasmic pH and the transmembrane potential. Therefore, the pump effectiveness in removing a particular drug molecule from the cell can be tuned by modifying the proton concentration gradient and the voltage drop across the membrane. Furthermore, we find that while both the proton concentration gradient across the membrane and the transmembrane potential contribute to the thermodynamic force driving the pump, their effects on the efflux enter not strictly in a combined proton motive force, but rather they have two distinguishable effects on the overall throughput. These results potentially explain the broad specificity of efflux pumps and suggest ways to overcome bacterial resistance, while highlighting unexpected effects of thermodynamic driving forces out of equilibrium.