A nat is a logarithmic unit of information

Information

Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

 or entropy

Information entropy

In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...

, based on natural logarithm

Natural logarithm

The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...

s and powers of e

E (mathematical constant)

The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...

, rather than the powers of 2 and base 2 logarithms

Binary logarithm

In mathematics, the binary logarithm is the logarithm to the base 2. It is the inverse function of n ↦ 2n. The binary logarithm of n is the power to which the number 2 must be raised to obtain the value n. This makes the binary logarithm useful for anything involving powers of 2,...

 which define the bit

Bit

A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

. The nat is the natural unit for information entropy. Physical systems of natural units which normalize Boltzmann's constant to 1 are effectively measuring thermodynamic entropy

Entropy

Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

 in nats.

When the Shannon entropy is written using a natural logarithm,


it is implicitly giving a number measured in nats.

One nat corresponds to about 1.44 bit

Bit

A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

s , or 0.434 ban

Ban (information)

A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit. As a bit corresponds to a binary digit, so a ban is a decimal digit...

s .

History

Alan Turing

Alan Turing

Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...

 used the natural ban

Ban (information)

A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit. As a bit corresponds to a binary digit, so a ban is a decimal digit...

(Hodges 1983, Alan Turing: The Enigma). Boulton and Wallace

Chris Wallace (computer scientist)

Professor Christopher Stewart Wallace was an Australian computer scientist notable for having devised:...

 (1970) used the term nit in conjunction with minimum message length

Minimum message length

Minimum message length is a formal information theory restatement of Occam's Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct...

 which was subsequently changed by the minimum description length

Minimum description length

The minimum description length principle is a formalization of Occam's Razor in which the best hypothesis for a given set of data is the one that leads to the best compression of the data. MDL was introduced by Jorma Rissanen in 1978...

 community to nat to avoid confusion with the nit

Nit (unit)

The candela per square metre is the derived SI unit of luminance. The unit is based on the candela, the SI unit of luminous intensity, and the square metre, the SI unit of area...

 used as a unit of luminance

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 or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

(Comley and Dowe, 2005, sec. 11.4.1, p271).