Comment on "Thermodynamics of Benford's first digit law" [Am. J. Phys. 87, 787–790 (2019)].

If HT <math display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"> </math> ht is a quantum of energy, HT <math display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow> N </mrow></math> ht represents the total energy of the system. This is reasonable because the key property of the Benford distribution is scale invariance.[4] Since HT <math display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"> </math> ht is our arbitrary unit of energy, it could be taken as small as we want, so that I N i would then go to infinity. Since HT <math display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub> k B </msub> T <mo></mo> </mrow></math> ht , we notice that HT <math display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mrow> N <mo></mo> I </mrow></math> ht . [Extracted from the article]