## Statistical Mechanics: A Short TreatiseThis book is the end result of a long story that started with my involvement as Coordinator of the Statistical Mechanics section of the Italian Encyclopedia of Physics. An Italian edition collecting several papers that I wrote for the Encyclo pedia appeared in September 1995, with the permission of the Encyclopedia and the sponsorship of Consiglio Nazionale delle Ricerche (CNR-GNFM). The present work is not a translation of the Italian version but it overlaps with it: an important part of it (Chaps. 1-3, 8) is still based on three arti cles written as entries for the Enciclopedia della Fisica (namely: "Meccanica Statistica", "Teoria degli Insiemi" and "Moto Browniano") which make up about 29% of the present book and, furthermore, it still contains (with little editing and updating) myoId review article on phase transitions (Chap. 6, published in La Rivista del Nuovo Cimento). In translating the ideas into English, I introduced many revisions and changes of perspective as well as new material (while also suppressing some other material). |

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### Contents

I | 1 |

II | 3 |

III | 10 |

IV | 14 |

V | 17 |

VI | 20 |

VII | 24 |

VIII | 27 |

XL | 182 |

XLI | 184 |

XLII | 188 |

XLIII | 189 |

XLIV | 192 |

XLV | 196 |

XLVI | 198 |

XLVII | 199 |

IX | 36 |

X | 44 |

XI | 48 |

XII | 57 |

XIII | 60 |

XIV | 68 |

XV | 73 |

XVI | 76 |

XVII | 84 |

XVIII | 89 |

XIX | 95 |

XX | 103 |

XXI | 107 |

XXII | 111 |

XXIII | 114 |

XXIV | 117 |

XXV | 129 |

XXVI | 136 |

XXVII | 142 |

XXVIII | 144 |

XXIX | 147 |

XXX | 153 |

XXXI | 155 |

XXXII | 157 |

XXXIII | 161 |

XXXIV | 167 |

XXXV | 172 |

XXXVI | 175 |

XXXVII | 176 |

XXXVIII | 178 |

XXXIX | 180 |

### Common terms and phrases

analysis Anosov map Anosov system average kinetic energy average value Boltzmann Boltzmann's equation boundary conditions Brownian motion called cellules chaotic hypothesis Chap classical statistical mechanics collisions computed consider constant correlation functions corresponding defined degrees of freedom denote density derivatives described dimension dynamics elements entropy equation equilibrium equivalence ergodic hypothesis evolution fact finite fixed fluctuation theorem formula free energy Gaussian given grand canonical ensemble hard core Hence implies integral interaction Ising model lattice magnetization Markov partition mathematical means microcanonical ensemble microscopic model of thermodynamics momentum number of particles observable orthodic ensembles parameters partition function permutation phase space cells phase transitions physical possible pressure probability distribution problem properties quantities quantum remark respect reversible sense sequence simple solution spin configuration SRB distribution stationary statistical ensembles surface symmetry T-particles temperature theory thermodynamic limit tions trajectory variables vectors velocity virial volume zero

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