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Boltzmann's Legacy
Edited by: Giovanni Gallavotti, University of Rome I, Italy, and Wolfgang L. Reiter and Jakob Yngvason, University of Vienna, Austria
A publication of the European Mathematical Society.
ESI Lectures in Mathematics and Physics
2007; 284 pp; hardcover
Volume: 5
ISBN-10: 3-03719-057-4
ISBN-13: 978-3-03719-057-9
List Price: US$78
Member Price: US$62.40
Order Code: EMSESILEC/5
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Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium "Boltzmann's Legacy" was held at the Erwin Schrödinger International Institute for Mathematical Physics in June 2006.

This text covers a broad spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of today's leading scholars in the field.

The book addresses students and researchers in mathematics, physics, and the history of science.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and research mathematicians interested in mathematical physics.

Table of Contents

  • G. Gallavotti -- Introduction
  • J. Renn -- Boltzmann and the end of the mechanistic worldview
  • E. H. Lieb -- What if Boltzmann had known about quantum mechanics
  • G. Gallavotti -- Entropy, nonequilibrium, chaos and infinitesimals
  • J. L. Lebowitz -- From time-symmetric microscopic dynamics to time-asymmetric macroscopic behavior: An overview
  • D. Ruelle -- What physical quantities make sense in nonequilibrium statistical mechanics?
  • D. S. Ornstein -- Boltzmann, ergodic theory, and chaos
  • C. Cercignani -- 134 years of Boltzmann equation
  • C. Villani -- \(H\)-theorem and beyond: Boltzman's entropy in today's mathematics
  • H. Spohn -- On the Boltzmann equation for weakly nonlinear wave equations
  • E. G. Cohen -- Entropy, probability and dynamics
  • C. Dellago and H. A. Posch -- Realizing Boltzmann's dream: computer simulations in modern statistical mechanics
  • A. Gabrielov, V. Keilis-Borok, Ya. Sinai, and I. Zaliapin< -- Statistical properties of the cluster dynamics of the systems of statistical mechanics
  • P. Schuster -- Boltzmann and evolution: some basic questions of biology seen with atomistic glasses
  • W. L. Reiter -- Ludwig Boltzmann--the restless prophet
  • Chronology
  • List of contributors
  • Name index
  • Subject index
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