Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium $φ^4$ Theory

We study nonequilibrium properties of a one-dimensional lattice Hamiltonian with quartic interactions in strong thermal gradients. Nonequilibrium temperature profiles, T(x), are found to develop significant curvature and boundary jumps. From the determination of the bulk thermal conductivity, we develop a quantitative description of T(x) including the jumps.