### Speaker

### Description

We consider one dimensional dynamics of interacting particles that have more conserved quantities that evolve macroscopically in the same diffusive time scale, and their macroscopic evolution is governed by a system of coupled diffusive equations. Their non-equilibrium stationary states, driven by heat bath and external forces, present interesting phenomena like up-hill diffusion, negative linear response, internal eternalizations (non-monotous temperature profiles). One example is given by the chain of coupled rotors. That conserves the energy and the angular momentum. Mathematical rigorous results can be obtained in harmonic chains of oscillators perturbed by noise that have more than one conservation laws. there are some common universal features due tothe transformation of mechanical work into thermal energy done by the bulk dynamics. Works in collaborations with Tomasz Komorowski, Marielle Simon, Alessandra Iacobucci, Gabriel Stoltz