World Library  
Flag as Inappropriate
Email this Article

Nat (unit)

Article Id: WHEBN0003070481
Reproduction Date:

Title: Nat (unit)  
Author: World Heritage Encyclopedia
Language: English
Subject: Entropy (information theory), Units of information, Hartley (unit), Pinsker's inequality, Information geometry
Publisher: World Heritage Encyclopedia

Nat (unit)

The natural unit of information (symbol nat),[1] sometimes also nit or nepit, is a 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. This unit is also known by its unit symbol, the nat. The nat is the natural unit for information entropy. Physical systems of natural units that normalize Boltzmann's constant to 1 are effectively measuring thermodynamic entropy in nats.

When the Shannon entropy is written using a natural logarithm,

H = - \sum_i p_i \ln p_i \!\,

it is implicitly giving a number measured in nats.

One nat is equal to 1/(ln 2) shannons ≈ 1.44 Sh or, equivalently, 1/(ln 10) hartleys ≈ 0.434 Hart.[2] The factors 1.44 and 0.434 arise from the relationships

\left (2^x=e^1\Rightarrow x=\tfrac{1}{\ln 2}\right ), and
\left (10^x=e^1\Rightarrow x=\tfrac{1}{\ln 10}\right ).

One nat is the information content of an event if the probability of that event occurring is 1/e.


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 used as a unit of luminance (Comley and Dowe, 2005, sec. 11.4.1, p271).


  1. ^ IEC 80000-13:2008
  2. ^
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.