Thomas Gilbert

Title: Heat conduction in stochastic energy exchange Markov jump processes with the gradient property

Abstract:  I will revisit the exactly solvable Kipnis-Marchioro-Presutti  model of heat flow and describe a systematic characterisation of non-equilibrium stationary states of systems of arbitrary sizes. These arguments yield a straightforward derivation of Fourier's law, different from that presented in the original KMP study, as well as higher-order static correlations, such as the elements of the covariant matrix. The transposition of these results to families of gradient models generalising the KMP model to many degrees of freedom will be discussed. When energy exchanges involve only a small fraction of the degrees of freedom at a time, we find that correlations collapse. The time-dependent distribution of energies then becomes of a product of local thermal equilibria whose temperatures evolve deterministically, even for systems of finite size.