### Abstract

Entropy was first introduced in 1865 by Rudolf Clausius in his study of the connection between work and heat. A mathematical definition was given by Boltzmann as the logarithm of the number of micro states that corresponds to a macro state. It plays important roles in statistical mechanics, in the theory of large deviations in probability, as an invariant in ergodic theory and as a useful tool in communication theory. This article explores some of the connections between these different contexts.

Original language | English (US) |
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Pages (from-to) | 1845-1857 |

Number of pages | 13 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 67 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2015 |

### Keywords

- Entropy
- Information
- Large deviations

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Varadhan, S. R. S. (2015). Entropy and its many Avatars.

*Journal of the Mathematical Society of Japan*,*67*(4), 1845-1857. https://doi.org/10.2969/jmsj/06741845