author={Jean Bricmont},
  journal={Annals of the New York Academy of Sciences},
  • J. Bricmont
  • Published 1 June 1995
  • Physics, Education
  • Annals of the New York Academy of Sciences
I try to clarify several confusions in the popular literature concerning chaos, determinism, the arrow of time, entropy and the role of probability in physics. Classical ideas going back to Laplace and Boltzmann are explained and defended while some recent views on irreversibility, due to Prigogine, are criticized. 

Chaos, Spatial Extension and Non-Equilibrium Thermodynamics

The connection between the statistical physics of transport phenomena and a microscopic description of the underlying chaotic motion has recently received new attention due to the convergence of

On the Foundations of Statistical Mechanics: Ergodicity, Many Degrees of Freedom and Inference

Why many degrees of freedom are necessary, while chaos is only marginally relevant, for the emergence of statistical laws in macroscopic systems is explained.

The Concept of Chaos in Contemporary Science: on Jean Bricmont's Critique of Ilya Prigogine's Ideas

Nonclarity around the understandingof the concept of chaos has caused someconfusion in the contemporary natural science.For instance, not making a clear distinctionbetween the deterministic and

The enigma of irreversibility and the interplay between Physics, Mathematics and Philosophy

The problem of reconciling a reversible micro-dynamics with the second law of thermodynamics has been a scientific and conceptual challenge for centuries and it continues to animate heated debate

KAM theory: The legacy of Kolmogorov’s 1954 paper

Kolmogorov-Arnold-Moser (or KAM) theory was developed for conservative dynamical systems that are nearly integrable. Integrable systems in their phase space usually contain lots of invariant tori,

On Microscopic Irreversibility and Non-deterministic Chaos: Resolving the Conflict between Determinism and Free Will

This article attempts to resolve the age-old conflict of determinism and free will. The problem is approached from two directions: biological information processing and physical determinism at the

A Field Guide to Recent Work on the Foundations of Statistical Mechanics.

This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility,

Emergent evolutionism, determinism and unpredictability.

Determinism, Chaos and Quantum Mechanics

After some general remarks on the notion of ”determinism”, I will discuss the precise meaning of chaos theory and the frequent misunderstandings concerning the implications of that theory. After



Randomness and Probability in Dynamical Theories: On the Proposals of the Prigogine School

I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of

Ergodicity, ensembles, irreversibility in Boltzmann and beyond

The contents of a not too well-known paper by Boltzmann are critically examined. The etymology of the word ergodic and its implications are discussed. A connection with the modern theory of Ruelle is

The second law of thermodynamics: entropy, irreversibility and dynamics

Irreversibility is at once a profound and an elusive concept. We are all aware of the directed, irreversible arrow of time which dominates our own existence. Until recently, however, it had been

Chance and Chaos

Chance probabilities mathematics and physics probabilities lotteries and horoscopes classical determinism games sensitive dependence on initial condition Hadamard, Duhem and Poincare turbulence -

The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations

The subjects treated here are part of an active and rapidly growing field of research that touches on the foundations of physics and chemistry. Specifically, the book presents, in as simple and

Time evolution of large classical systems

We begin with some very general and elementary remarks about nonequilibrium statistical mechanics. We then establish our notation for discussing finite systems of classical point particles, construct

The recently recognized failure of predictability in Newtonian dynamics

  • M. Lighthill
  • Physics, Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1986
Modern theories of dynamical systems have very clearly demonstrated the unexpected fact that systems governed by the equations of Newtonian dynamics do not necessarily exhibit the ‘predictability’

Boltzmann's Entropy and Time's Arrow

Given the success of Ludwig Boltzmann's statistical approach in explaining the observed irreversible behavior of macroscopic systems in a manner consistent with their reversible microscopic dynamics,

Cracks in the glass menagerie of science

Time and time again reputable scientists have disagreed with some part of accepted scientific doctrine. And one thing they can then do is write a book for the general public, letting us have a piece

Modern ergodic theory

The founding fathers of statistical mechanics, Boltzmann, Maxwell, Gibbs and Einstein, invented the concept of ensembles to describe equilibrium and nonequilibrium macroscopic systems. In trying to