Related on Lably
Through Information, Natural logarithm and Luminance
One nat is equal to 1/ln 2 shannons ≈ 1.44 Sh or, equivalently, 1/ln 10 hartleys ≈ 0.434 Hart.
History
Boulton and Wallace used the term nit in conjunction with minimum message length, which was subsequently changed by the minimum description length community to nat to avoid confusion with the nit used as a unit of luminance.
Alan Turing used the term natural ban with the same meaning.
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Entropy
Shannon entropy (information entropy), being the expected value of the information of an event, is inherently a quantity of the same type and with a unit of information. The International System of Units, by assigning the same unit (joule per kelvin) both to heat capacity and to thermodynamic entropy implicitly treats information entropy as a quantity of dimension one, with 1 nat = 1. Systems of natural units that normalize the Boltzmann constant to 1 are effectively measuring thermodynamic entropy with the nat as unit.
When the Shannon entropy is written using a natural logarithm, it is implicitly giving a quantity with nat as the unit.