Chapter 19. Generalization of the Fluctuation–Dissipation Theorem for Excess Heat Production

  1. M. Toda3,
  2. T. Komatsuzaki4,
  3. T. Konishi5,
  4. R. S. Berry6 and
  5. S. A. Rice7
  1. Hiroshi H. Hasegawa1,2 and
  2. Yoshikazu Ohtaki1

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch19

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

How to Cite

Hasegawa, H. H. and Ohtaki, Y. (2005) Generalization of the Fluctuation–Dissipation Theorem for Excess Heat Production, in Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130 (eds M. Toda, T. Komatsuzaki, T. Konishi, R. S. Berry and S. A. Rice), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471712531.ch19

Editor Information

  1. 3

    Physics Department, Nara Women's University, Nara, 630-8506, Japan

  2. 4

    Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan

  3. 5

    Department of Physics, Nagoya University, Nagoya, 464-8602, Japan

  4. 6

    Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA

  5. 7

    Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

Author Information

  1. 1

    Department of Mathematical Sciences, Ibaraki University, Mito, 310-8512, Japan

  2. 2

    Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, Austin, Texas 78712, USA

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 21 JAN 2005

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. Stuart A. Rice

Series Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

ISBN Information

Print ISBN: 9780471711582

Online ISBN: 9780471712534

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Keywords:

  • thermodynamics;
  • fluctuation-dissipation theorem;
  • adiabatic invariant;
  • superstatistics

Summary

We continue our study of the fluctuation-dissipation theorem for excess heat production. The theorem is based on the Boltzmann equilibrium distribution. We generalize it for two typical equilibrium distributions in this paper. One is the superstatistical equilibrium distribution including the Tsallis distribution. The other is the micro-canonical distribution in which we reconsider adiabatic invariance. We numerically find that the non-ergodic adiabatic invariant for a Hamiltonian chaotic system is broken in the mixing phase space.