Special Session 102:
 Quantitative Rates of Convergence to Non-Equilibrium Steady States for the Chain of Oscillators
 Angeliki Menegaki University of Cambridge, UKGreece Co-Author(s):
 Abstract: A long-standing issue in the study of out-of-equilibrium systems in statistical mechanics is the validity of Fourier`s law. In this talk we will present a model introduced for this purpose, i.e. to describe properly heat diffusion. It consists of a $1$-dimensional chain of $N$ oscillators coupled at its ends to heat baths at different temperatures. Here, working with a weakly anharmonic homogeneous chain, we will show how it is possible to prove exponential convergence to the non-equilibrium steady state in Wasserstein-$2$ distance and in Relative Entropy. The method we follow is a generalised version of the theory of $\Gamma$ calculus. It has the advantage to give quantitative results, thus we will discuss how the convergence rates depend on the number of the particles $N$.