Boltzmann's legacy [the International Symposium "Boltzmann's Legacy" was held at the Erwin Schrödinger International Institute for Mathematical Physics in June 2006

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 Schrodinger 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. Cover......Page 1 Ludwig Boltzmann (1844–1906......Page 3 Boltzmann’s Legacy......Page 4 ISBN 978-3-03719-057-9......Page 5 Foreword......Page 6 Contents......Page 8 Introduction by Giovanni Gallavotti......Page 10 Boltzmann and the end of the mechanistic worldview by Jürgen Renn......Page 16 What if Boltzmann had known about quantum mechanics by Elliott H. Lieb......Page 36 Entropy, nonequilibrium, chaos and infinitesimals by Giovanni Gallavotti......Page 48 From time-symmetric microscopic dynamics to time-asymmetric macroscopic behavior: an overview by Joel L. Lebowitz......Page 72 What physical quantities make sense in nonequilibrium statistical mechanics? by David Ruelle......Page 98 Boltzmann, ergodic theory, and chaos by Donald S. Ornstein......Page 108 134 years of Boltzmann equation by Carlo Cercignani......Page 116 H-theorem and beyond: Boltzmann’s entropy in today’s mathematics by Cédric Villani......Page 138 On the Boltzmann equation for weakly nonlinear wave equations by Herbert Spohn......Page 154 Entropy, probability and dynamics by E. G. D. Cohen......Page 170 Realizing Boltzmann’s dream: computer simulations in modern statistical mechanics by Christoph Dellago and Harald A. Posch......Page 180 Statistical properties of the cluster dynamics of the systems of statistical mechanics by A. Gabrielov, V. Keilis-Borok,Ya. Sinai, and I. Zaliapin......Page 212 Boltzmann and evolution: some basic questions of biology seen with atomistic glasses by Peter Schuster......Page 226 Ludwig Boltzmann – the restless prophet by Wolfgang L. Reiter......Page 252 Chronology......Page 270 List of contributors......Page 274 Name index......Page 276 Subject index......Page 280 Back Cover......Page 286 TeX output 2008.08.03:0953 Cover 1 Ludwig Boltzmann (1844–1906 3 Title 4 Boltzmann’s Legacy 4 Copyright 5 © 2008 European Mathematical Society 5 ISBN 978-3-03719-057-9 5 Foreword 6 Contents 8 Introduction by Giovanni Gallavotti 10 Boltzmann and the end of the mechanistic worldview by Jürgen Renn 16 What if Boltzmann had known about quantum mechanics by Elliott H. Lieb 36 Entropy, nonequilibrium, chaos and infinitesimals by Giovanni Gallavotti 48 From time-symmetric microscopic dynamics to time-asymmetric macroscopic behavior: an overview by Joel L. Lebowitz 72 What physical quantities make sense in nonequilibrium statistical mechanics? by David Ruelle 98 Boltzmann, ergodic theory, and chaos by Donald S. Ornstein 108 134 years of Boltzmann equation by Carlo Cercignani 116 H-theorem and beyond: Boltzmann’s entropy in today’s mathematics by Cédric Villani 138 On the Boltzmann equation for weakly nonlinear wave equations by Herbert Spohn 154 Entropy, probability and dynamics by E. G. D. Cohen 170 Realizing Boltzmann’s dream: computer simulations in modern statistical mechanics by Christoph Dellago and Harald A. Posch 180 Statistical properties of the cluster dynamics of the systems of statistical mechanics by A. Gabrielov, V. Keilis-Borok,Ya. Sinai, and I. Zaliapin 212 Boltzmann and evolution: some basic questions of biology seen with atomistic glasses by Peter Schuster 226 Ludwig Boltzmann – the restless prophet by Wolfgang L. Reiter 252 Chronology 270 List of contributors 274 Name index 276 Subject index 280 Back Cover 286 Introduction / Giovanni Gallavotti -- Boltzmann And The End Of The Mechanistic Worldview / Jürgen Renn -- What If Boltzmann Had Known About Quantum Mechanics / Elliott H. Lieb -- Entropy, Nonequilibrium, Chaos And Infinitesimals / Giovanni Gallavotti -- From Time-symmetric Microscopic Dynamics To Time-asymmetric Macroscopic Behavior: An Overview / Joel L. Lebowitz -- What Physical Quantities Make Sense In Nonequilibrium Statistical Mechanics? / David Ruelle -- Boltzmann, Ergodic Theory, And Chaos / Donald S. Ornstein -- 134 Years Of Boltzmann Equation / Carlo Cercignani -- H-theorem And Beyond: Boltzmann's Entropy In Today's Mathematics / Cédric Villani -- On The Boltzmann Equation For Weakly Nonlinear Wave Equations / Herbert Spohn -- Entropy, Probability And Dynamics / E.g.d. Cohen -- Realizing Boltzmann's Dream: Computer Simulations In Modem Statistical Mechanics / Christoph Dellago And Harald A. Posch -- Statistical Properties Of The Cluster Dynamics Of The Systems Of Statistical Mechanics / A. Gabrielov [and Others] -- Boltzmann And Evolution: Some Basic Questions Of Biology Seen With Atomistic Glasses / Peter Schuster -- Ludwig Boltzmann -- The Restless Prophet / Wolfgang L. Reiter. Giovanni Gallavotti, Wolfgang L. Reiter, Jakob Yngvason, Editors. Includes Bibliographical References And Indexes. 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"#x9D; was held at the Erwin Schrödinger International Institute for Mathematical Physics in June 2006. This text covers a wide 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 present day's leading scholars in the field. The book addresses students and researchers in mathematics, physics and the history of science