Heat conduction in chains of nonlinear oscillators

We numerically study heat conduction in chains of nonlinear oscillators with time-reversible thermostats. A nontrivial temperature profile is found to set in, which obeys a simple scaling relation for increasing the number N of particles. The thermal conductivity diverges approximately as N-1/2, indicating that chaotic behavior is not enough to ensure the Fourier law. Finally, we show that the microscopic dynamics ensures fulfillment of a macroscopic balance equation for the entropy production.