A nat (sometimes also nit or even nepit) is a logarithmic unit of information or entropy, based on natural logarithms and powers of e, rather than the powers of 2 and base 2 logarithms which define the bit. The nat is the natural unit for information entropy, corresponding to Boltzmann's constant for thermodynamic entropy. Logarithmic units are abstract mathematical units that can be used to express any quantities (physical or mathematical) that are defined on a logarithmic scale, that is, as being proportional to the value of a logarithm function. ... Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ... Entropy of a Bernoulli trial as a function of success probability. ... The natural logarithm is the logarithm to the base e, where e is equal to 2. ... The mathematical constant e is the base of the natural logarithm. ... Plot of log2 x In mathematics, the binary logarithm (log2 n) is the logarithm for base 2. ... This article is about the unit of information. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... Ice melting - a classic example of entropy increasing In thermodynamics, thermodynamic entropy (or simply entropy) is an important state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. ...

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 bits (log₂(e)), or 0.434 hartleys (log₁₀(e)). This article is about the unit of information. ... A ban, sometimes called a hartley, 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. ...

History

Alan Turing used the natural ban (Hodges 1983, Alan Turing: The Enigma.). Boulton and Wallace (1970) 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 (unit) (Comley and Dowe, 2005, sec. 11.4.1, p271). Alan Turing is often considered the father of modern computer science. ... A ban, sometimes called a hartley, 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. ... Professor Christopher Stewart Wallace (26 October 1933—7 August 2004) was an Australian computer scientist (and physicist, etc. ... Minimum message length (MML) is a formal information theory restatement of Occams 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 (where the message consists of a statement of... The minimum description length principle is a formalization of Occams Razor in which the best hypothesis for a given set of data is the one that leads to the largest compression of the data. ... This article is about the unit of measure. ...

References

• J.W. Comley and D.L. Dowe, ``Minimum Message Length, MDL and Generalised Bayesian Networks with Asymmetric Languages, Chapter 11 (pp265-294) in P. Grünwald, I. J. Myung and M. A. Pitt (eds.), `Advances in Minimum Description Length: Theory and Applications', MIT Press (ISBN 0-262-07262-9), April 2005.
• Fazlollah M. Reza. An Introduction to Information Theory. New York: Dover 1994. ISBN 048668210