Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-01-10
Physics
Condensed Matter
Statistical Mechanics
78 pages, 11 figures, submitted to Studies in History and Philosophy of Modern Physics
Scientific paper
In the second half of the 19th century, the kinetic theory of gases has probably raised one of the most impassioned debates in the history of science. The so-called reversibility paradox around which intense polemics occurred reveals the apparent incompatibility between the microscopic and macroscopic levels. While classical mechanics describes the motion of bodies such as atoms and molecules by means of time reversible equations, thermodynamics emphasizes the irreversible character of macroscopic phenomena such as viscosity. Aiming at reconciling both levels of description, Boltzmann proposed a probabilistic explanation. Nevertheless, such an interpretation has not totally convinced generations of physicists, so that this question has constantly animated the scientific community since his seminal work. In this context, an important breakthrough in dynamical systems theory has shown that the hypothesis of microscopic chaos played a key role and provided a dynamical interpretation of the emergence of irreversibility. Using viscosity as a leading concept, we sketch the historical development of the concepts related to this fundamental issue up to recent advances. Following the analysis of the Liouville equation introducing the concept of Pollicott-Ruelle resonances, two successful approaches --- the escape-rate formalism and the hydrodynamic-mode method --- establish remarkable relationships between transport processes and chaotic properties of the underlying Hamiltonian dynamics.
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