A deep chasm still separates the microscopic world of atoms and molecules from the familiar macroscopic world that is part of everyday life. These worlds are profoundly different. In the former, time is reversible and the dynamics is Hamiltonian whereas, in the latter, we see dissipation, increasing entropy, and a very definite arrow of time.For equilibrium systems, Boltzmann’s revolutionary ideas of a century ago provide deep insight, and have stood the test of time. Supplemented by the quantum statistical mechanics that came later, they lead to an excellent description of large-scale behaviour based on properties at the atomic and molecular scale. Thus, equilibrium thermodynamics can be derived convincingly from statistical mechanics, with only a few leaps of faith along the way. The only requirement is that the number of particles should be large. For non-equilibrium and open systems, however, there are few such certainties. The discovery (or rediscovery) of dynamical chaos added a further dimension to the problem, because the statistical features typically observed in systems with many degrees of freedom can also be generated by deterministic chaos in simple systems. So what is the connection, if any?
Review of book "Chaos and Coarse Graining in Statistical Mechanics", by P. Castiglione, M. Falcioni, A. Lesne and A. Vulpian.