Renewable energy driven electrolytic water splitting is a required technology for low-carbon hydrogen production to achieve the goal of net-zero CO2 emission by 2050. This technology also serves as a necessary energy storage route to resolve the intolerable intermittency and unreliability issues of renewable energies. The prevailing of this hydrogen production technology however is restricted by the high cost of electricity. Consequently, developments of cost–effective highly efficient and stable electrocatalysts to drive the electrolytic water splitting reactions are the key. In terms of catalyst developments, mono-component systems are first explored, followed by multi–component systems, taking advantages of possible positive synergy between constituent components. Recently, a new class of multi-component catalyst systems, entropy-stabilized materials, including alloys, oxides, sulfides, phosphides, etc., emerges and is demonstrated promising performances toward electrocatalysis. In light of the variable and flexible element compositions, entropy-stabilized materials provide infinite and enormous potentials for the design of promising electrocatalysts. The key is to maximize the synergy between constituent components. High entropy alloys (HEA), defined as alloys composed of five or more major metallic elements, have been under intensive and extensive development in past fifteen years for their extraordinary mechanical, magnetic, corrosion, and catalytic properties. Herein, an equi–molar FeCoNiCuMo HEA on nickel foam was developed as a breakthrough catalyst for electrocatalytic water splitting, in terms of both activity and stability, in pH-universal media and in severe industrial operation conditions. Furthermore, a new catalytic phenomenon is discovered. Two different catalytic mechanisms function simultaneously on different constituents of the catalyst, and the synergistic interactions between the two categorical domains leads to catalytic kinetics faster than the theoretical limit set by a single rate-limiting step, Tafel step of the Volmer-Tafel route. A new kinetic model is developed to predict a new theoretical lower limit of Tafel slopes of 15 mV/dec based on a synergistic interaction between the two categorical domains of the high entropy alloy catalyst. This new development proves that the theoretical lower limit of Tafel slope of 30 mV/dec posed for the Volmer-Tafel mechanism functioning on a single component catalyst can be further reduced to 15 mV/dec through synergistic interactions between two categorical domains of a multi-component catalyst. It is demonstrated that high entropy materials, composed of five or more atomically/molecularly well-mixed major components, are intrinsically promising candidates for realization of quantum leaps in catalytic performances of catalysts.