## Dynamics and Thermodynamics of Systems with Long Range InteractionsThierry Dauxois, Stefano Ruffo, Ennio Arimondo, Martin Wilkens Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose--Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student. |

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### Contents

1 | |

Thermostatistics or Topology of the Microcanonical Entropy Surface | 20 |

Ensemble Inequivalence in MeanField Models of Magnetism | 45 |

Phase Transitions in Finite Systems | 68 |

Phase Transitions in Systems with 1rα Attractive Interactions | 130 |

From LowDimensional Maps to Hamiltonian Systems | 140 |

Statistical Mechanics of Gravitating Systems in Static and Cosmological Backgrounds | 163 |

Statistical Mechanics of TwoDimensional Vortices and Stellar Systems | 208 |

Ultracold Atoms and BoseEinstein Condensates in Optical Lattices | 312 |

Canonical Statistics of Occupation Numbers for Ideal and Weakly Interacting BoseEinstein Condensates | 332 |

New Regimes in Cold Gases via LaserInduced LongRange Interactions | 369 |

Dynamics and Selfconsistent Chaos in a Mean Field Hamiltonian Model | 404 |

Kinetic Theory for Plasmas and WaveParticle Hamiltonian Dynamics | 437 |

Emergence of Fractal Clusters in Sequential Adsorption Processes | 448 |

From Dynamics to Statistical Mechanics and Back | 458 |

489 | |

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### Common terms and phrases

approximation atoms average beams Bose Bose gas Bose–Einstein condensates calculated caloric curve canonical ensemble coherent configuration consider constant corresponds Dauxois defined density described diffusion discussed dynamics entropy equation equilibrium evolution finite systems fluctuations free energy frequency gravitating systems gravitational clustering Hamiltonian HMF model initial conditions integral Ising model kinetic energy laser Lett linear logistic map long-range interactions Lyapunov exponent magnetization mean field microcanonical ensemble momentum negative heat capacity negative specific heat nonlinear number of particles obtained optical lattice order parameter order phase transition oscillator P.H. Chavanis partition sum phase diagram phase space Phys Physics plasma point vortices quantum regime region relation relaxation rotation scales Sect self-consistent self-gravitating systems solution statistical mechanics structure superfluid systems with long-range temperature theory thermodynamic limit transform trap tricritical point Tsallis variables velocity vortex zero