noindent ``Coupled particle and heat transport: a dynamical system's perspective'' \ \ ABSTRACT: \ The understanding of coupled particle and heat transport in complex systems is a fundamental problem, also of practical interest in connection with the challenging task of developing high-performance thermoelectric materials. I will discuss thermoelectric transport phenomena from the perspective of dynamical nonlinear systems, trying to unveil microscopic mechanisms that can lead to high thermoelectric efficiency [1]. In particular, I will show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result will be illustrated by means of a diatomic chain of hard-point elastically colliding particles and in a two-dimensional multiparticle collision dynamics model, where the total momentum is the only relevant conserved quantity [2]. I will then focus on the efficiency of three-terminal thermoelectric transport under broken time-reversal symmetry, showing that the Curzon-Ahlborn limit can be exceeded within linear response in an Aharonov-Bohm interferometer model and that a more abstract transmission model saturates the upper bound for efficiency in non-interacting systems [3]. \ \ References: \ {}[1] G. Benenti and G. Casati, Increasing thermoelectric efficiency: dynamical models unveil microscopic mechanisms, Phil. Trans. R. Soc. A 369, 466 (2011). \ {}[2] G. Benenti, G. Casati and J. Wang, Conservation laws and thermodynamic efficiencies, Phys. Rev. Lett. 110, 070604 (2013). \ {}[3] V. Balachandran, G. Benenti and G. Casati, Efficiency of three-terminal thermoelectric transport under broken-time reversal symmetry, Phys. Rev. B 87, 165419 (2013).