t-mixing: from fluctuation relations to response and irreversibility in MD

This paper provides an introduction to the theory of steady-state fluctuation relations for molecular dynamics systems, that led to a general theory of response. The main ingredient of this theory is a new dynamical condition now known as t-mixing. We use such a condition to identify necessary and sufficient conditions for the relaxation to a steady state (whether equilibrium or not) of an ensemble of identical systems, as well as of a single system. This allows us to address the problem of the irreversibility of time reversal invariant (conservative as well as dissipative) particle systems.