Conservation Laws and Thermodynamic Efficiencies

The understanding of the microscopic mechanisms which determine the macroscopic laws of heat and particles transport is one of the main problems of statistical mechanics. On the other hand, thermoelectric phenomena, which involve the conversion between thermal and electrical energy, and provide a method for heating and cooling materials, are expected to play an increasingly important role in meeting the energy challenge of the future. Here we discuss a new approach to this problem, which is rooted in nonlinear dynamical systems. More precisely we will discuss idealized models of interacting particles in one and two dimensions