Deviation from local equilibrium distribution in one-dimensional lattice thermal conduction

We study the single-particle momentum distribution functions of a one-dimensional Hamiltonian system in the nonequilibrium steady state of heat conduction. Deviation from the Maxwellian distribution is measured by the use of the relative entropy. As a result, it is found that the total relative entropy linearly increases with the system size in an integrable model, while it decreases for large N in nonintegrable systems. Moreover, effects of a symmetry are discussed and some differences are found between the FPU model and the phi(4) model when the boundary breaks the symmetry.