The Steenbeck minimum voltage（SMP） is widely used in the study of arc discharge plasmas

however

its validity is still in dispute in history. Consequently

we reexamined and discussed the history of SMP

and analyzed the true mathematical and physical meanings of the SMP in detail. Results show that the original method combined with SMP and Steenbeck’s channel model（SCM） tends to give a wrong estimation of the arc channel radius. On the other hand

analyses show that the SMP is redundant in the characterization of arc discharge plasma

after comparing it with other model or method on the solution of energy equation（also called the Elenbaas-Heller equation）. In the end

the relation and difference between SMP and the classical thermodynamic-electromagnetic theory

including the minimum entropy production principle（MEP） and so on

is discussed.