Heat conduction in one-dimensional lattice dynamical systems far from   equilibrium
  We study heat conduction in one dimensional lattice dynamical systems far from equilibrium. The Fermi-Pasta-Ulam model and the $\phi^4$ model are numerically compared to elucidate differences between momentum-conserving and nonconserving systems. As a results, it is found that the heat flux in the $\phi^4$ model does not increase monotonically as the temperature differences at the ends of the lattice is increased, while it does in the FPU chain. 
Akira Ueda and Shinji Takesue