C. Bernardin, Hydrodynamics for a system of harmonic oscillators perturbed by a conservative noise, Stochastic Processes and their Applications, vol.117, pp.487-513, 2007.

C. Bernardin, Heat conduction model: stationary non-equilibrium properties, Physical Review E 78, 2008.

C. Bernardin, V. Kannan, J. L. Lebowitz, and J. Lukkarinen, Harmonic Systems with Bulk Noises, Journal of Statistical Physics, vol.146, pp.800-831, 2012.
URL : https://hal.archives-ouvertes.fr/ensl-00635335

C. Bernardin and S. Olla, Fourier Law for a Microscopic Model of Heat Conduction, J. Stat. Phys, vol.121, pp.271-289, 2005.

C. Bernardin and S. Olla, Transport Properties of a Chain of Anharmonic Oscillators with Random Flip of Velocities, J. Stat. Phys, vol.145, pp.1224-1255, 2011.
URL : https://hal.archives-ouvertes.fr/ensl-00589672

A. Bradji and R. Herbin, Discretization of the coupled heat and electrical diffusion problems by the finite element and the finite volume methods, IMA Journal of Numerical Analysis, vol.28, issue.3, pp.469-495, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00123247

M. Colangeli, A. De-masi, and E. Presutti, Microscopic models for uphill diffusion, Journal of Physics A: Mathematical and Theoretical, vol.50, issue.43, 2017.

N. Even and S. Olla, Hydrodynamic Limit for an Hamiltonian System with Boundary Conditions and Conservative Noise, Arch. Rat. Mech. Appl, vol.213, pp.61-585, 2014.

L. Hörmander, Hypoelliptic second order differential equations, Acta Math, vol.119, pp.147-171, 1967.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, Negative thermal conductivity of chains of rotors with mechanical forcing, Phys. Rev. E, vol.84, p.61108, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00608036

S. Iubini, S. Lepri, R. Livi, and A. Politi, Boundary induced instabilities in coupled oscillators, Phys. Rev. Lett, vol.112, p.134101, 2014.

M. Jara, T. Komorowski, and S. Olla, Superdiffusion of Energy in a system of harmonic oscillators with noise, Commun. Math. Phys, vol.339, p.407, 2015.

J. L. Kelley, General topology, 1991.

C. Kipnis and C. Landim, Scaling Limits of Interacting Particle Systems, 1999.

T. Komorowski and S. Olla, Diffusive propagation of energy in a non-acoustic chain, Arch. Rat. Mech. Appl, vol.223, issue.1, pp.95-139, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01253315

T. Komorowski, S. Olla, and M. Simon, Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities, Kinetic and Related Models, vol.11, pp.615-645, 2018.

R. Krishna, Uphill diffusion in multicomponent mixtures, Chem. Soc. Rev, vol.44, pp.2812-2836, 2015.

S. Lepri, R. Livi, and A. Politi, Thermal Conduction in classical low-dimensional lattices, Phys. Rep, vol.377, pp.1-80, 2003.

S. Lepri, R. Livi, and A. Politi, Heat conduction in chains of nonlinear oscillators, Phys. Rev. Lett, vol.78, p.1896, 1997.

V. Letizia and S. Olla, Non-equilibrium isothermal transformations in a temperature gradient from a microscopic dynamics, with V. Letizia, Annals of Probability, vol.45, pp.3987-4018, 2017.

S. Olla, Role of conserved quantities in Fourier's law for diffusive mechanical systems, Comptes Rendus Physiques, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02157554

H. Spohn, Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains, Journal of Statistical Physics, vol.154, 2013.

T. Komorowski,

S. Olla, :. Cnrs, C. , and U. Paris-dauphine, , vol.75016