Final Report Summary - MPOES (Mathematical Physics of Out-of-Equilibrium Systems)
How do macroscopic laws of matter emerge from the motion of its microscopic constituents? The fundamental laws governing the micro-world of atoms and molecules are reversible in time: future can not be distinguished from the past. On the macroscopic level this is no longer true. Macroscopic motion exhibits friction and dissipation. Heat flows from hot to cold and not vice versa. Our understanding of these issues on a mathematical level is still very incomplete. Our project has contributed to this understanding. We have studied these issues on several levels: rigorous mathematics, theoretical physics and numerical simulations. On the fundamental level we have succeeded giving mathematically rigorous proofs of dissipation in deterministic time reversible dynamical models of microscopic world. We have derived and studied the properties of the various macroscopic equations in a variety of contexts such as normal and anomalous transport of heat as well as electrical insulation, conduction and super conduction.