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Large Deviations in Physics

The Legacy of the Law of Large Numbers

  • Book
  • © 2014

Overview

Editors:
  1. Angelo Vulpiani

    1. Dipartimento di Fisica, Università di Roma Sapienza, Roma, Italy

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  2. Fabio Cecconi

    1. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

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  3. Massimo Cencini

    1. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

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  4. Andrea Puglisi

    1. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

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  5. Davide Vergni

    1. Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy

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  • Gives a unifying view of large deviations
  • Presents modern aspects of equilibrium and non-equilibrium statistical physics, disordered and chaotic systems and turbulence
  • Covers both theory and applications
  • Discusses numerical aspects in detail
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 885)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiv
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  2. From the Law of Large Numbers to Large Deviation Theory in Statistical Physics: An Introduction

    • Fabio Cecconi, Massimo Cencini, Andrea Puglisi, Davide Vergni, Angelo Vulpiani
    Pages 1-27

  3. Ergodicity: How Can It Be Broken?

    • Giancarlo Benettin, Roberto Livi, Giorgio Parisi
    Pages 29-70

  4. Large Deviations in Stationary States, Especially Nonequilibrium

    • Giovanni Jona-Lasinio
    Pages 71-92

  5. Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium and Back

    • Paolo Adamo, Roman Belousov, Lamberto Rondoni
    Pages 93-133

  6. Large Deviations in Disordered Spin Systems

    • Andrea Crisanti, Luca Leuzzi
    Pages 135-160

  7. Large Deviations in Monte Carlo Methods

    • Andrea Pelissetto, Federico Ricci-Tersenghi
    Pages 161-191

  8. Large Deviations Techniques for Long-Range Interactions

    • Aurelio Patelli, Stefano Ruffo
    Pages 193-220

  9. Large Deviations of Brownian Motors

    • Alessandro Sarracino, Dario Villamaina
    Pages 221-241

  10. Stochastic Fluctuations in Deterministic Systems

    • Antonio Politi
    Pages 243-261

  11. Anomalous Diffusion: Deterministic and Stochastic Perspectives

    • Roberto Artuso, Raffaella Burioni
    Pages 263-293

  12. Large Deviations in Turbulence

    • Guido Boffetta, Andrea Mazzino
    Pages 295-310

  13. Back Matter

    Pages 311-314
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Keywords

About this book

This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.

Editors and Affiliations

  • Dipartimento di Fisica, Università di Roma Sapienza, Roma, Italy

    Angelo Vulpiani

  • Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

    Fabio Cecconi, Massimo Cencini, Andrea Puglisi

  • Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy

    Davide Vergni

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