### 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) |
---|---|

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 - 2015 |

### Fingerprint

### Keywords

- Entropy
- Information
- Large deviations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Mathematical Society of Japan*,

*67*(4), 1845-1857. https://doi.org/10.2969/jmsj/06741845

**Entropy and its many Avatars.** / Varadhan, Srinivasa.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 67, no. 4, pp. 1845-1857. https://doi.org/10.2969/jmsj/06741845

}

TY - JOUR

T1 - Entropy and its many Avatars

AU - Varadhan, Srinivasa

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Entropy

KW - Information

KW - Large deviations

UR - http://www.scopus.com/inward/record.url?scp=84947081288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947081288&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06741845

DO - 10.2969/jmsj/06741845

M3 - Article

VL - 67

SP - 1845

EP - 1857

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 4

ER -