The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of

information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random, ...

, based on

natural logarithms The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, i ...

and powers of ''e'', rather than the powers of 2 and base 2 logarithms, which define the shannon. This unit is also known by its unit symbol, the nat. One nat is the information content of an event when the probability of that event occurring is 1/ ''e''. One nat is equal to shannons ≈ 1.44 Sh or, equivalently, hartleys ≈ 0.434 Hart.

History

Boulton and

Wallace Wallace may refer to: People * Clan Wallace in Scotland * Wallace (given name) * Wallace (surname) * Wallace (footballer, born 1986), full name Wallace Fernando Pereira, Brazilian football left-back * Wallace (footballer, born 1987), full name ...

used the term ''nit'' in conjunction with minimum message length, which was subsequently changed by the

minimum description length Minimum Description Length (MDL) is a model selection principle where the shortest description of the data is the best model. MDL methods learn through a data compression perspective and are sometimes described as mathematical applications of Occa ...

community to ''nat'' to avoid confusion with the nit used as a unit of

luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls with ...

Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical ...

used the ''natural

ban Ban, or BAN, may refer to: Law * Ban (law), a decree that prohibits something, sometimes a form of censorship, being denied from entering or using the place/item ** Imperial ban (''Reichsacht''), a form of outlawry in the medieval Holy Roman ...

''.

Entropy

Shannon entropy Shannon may refer to: People * Shannon (given name) * Shannon (surname) * Shannon (American singer), stage name of singer Shannon Brenda Greene (born 1958) * Shannon (South Korean singer), British-South Korean singer and actress Shannon Arrum W ...

(information entropy), being the

expected value In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...

of the information of an event, is a quantity of the same type and with the same units as information. The

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

, by assigning the same units (

joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...

per

kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...

) both to

heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat cap ...

and to thermodynamic entropy implicitly treats information entropy as a

quantity of dimension one A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or ...

, with . Physical systems of natural units that normalize the

Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...

to 1 are effectively measuring thermodynamic entropy in nats. When the Shannon entropy is written using a natural logarithm,

\Eta = - \sum_i p_i \ln p_i

it is implicitly giving a number measured in nats.

History

Entropy

Notes

References

Further reading