  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.
