## Asymmetry: The Foundation of InformationAs individual needs have arisen in the fields of physics, electrical engineering and computational science, each has created its own theories of information to serve as conceptual instruments for advancing developments. This book provides a coherent consolidation of information theories from these different fields. The author gives a survey of current theories and then introduces the underlying notion of symmetry, showing how information is related to the capacity of a system to distinguish itself. A formal methodology using group theory is employed and leads to the application of Burnside's Lemma to count distinguishable states. This provides a versatile tool for quantifying complexity and information capacity in any physical system. Written in an informal style, the book is accessible to all researchers in the fields of physics, chemistry, biology, computational science as well as many others. |

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### Contents

1 | |

Information | 5 |

22 A Survey of Information Theories | 6 |

221 Thermodynamic Information Theory | 7 |

222 Information Communication Theory | 32 |

223 Algorithmic Information Theory | 34 |

224 Signpost | 54 |

23 Probability | 56 |

44 Information and Probability | 100 |

45 Information and Statistical Mechanics | 112 |

452 Demonic Information | 116 |

46 Information and Physical Thermodynamics | 118 |

462 Symmetry and the Third Law | 120 |

463 Information and The Gibbs Paradox | 122 |

47 Quantum Information | 124 |

471 Quantum Information and Distinguishability | 125 |

231 Subjective Probability | 57 |

233 Dispositional Probability | 63 |

24 Signpost | 65 |

Information and Distinguishability | 67 |

A Foundational Approach | 76 |

Information and Symmetry | 79 |

42 Symmetry and Group Theory | 81 |

421 Subgroups and Special Groups | 87 |

422 Group Theory and Information | 89 |

43 Symmetry and Information | 96 |

431 Information Generation | 97 |

432 Extrinsic and Intrinsic Information | 99 |

48 Symmetries and Algorithmic Information Theory | 132 |

483 Groups and Algorithmic Information Theory | 133 |

484 Symmetry and Randomness | 137 |

485 A Final Signpost | 141 |

Conclusion | 143 |

Burnsides Lemma | 147 |

Worked Examples | 149 |

B13 Case 3 | 152 |

B2 Binary String | 153 |

155 | |

161 | |