Microscopic chaos is the dynamical randomness in the collisional motion of atoms and molecules in fluids. This chaos animates different mesoscopic stochastic phenomena and, in particular, the reaction-diffusion processes. For different chemical reactions, we show how the reaction rate can be...

An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation toward a state of equilibrium can be derived from...

A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random numbers of particles in cells of given position and...