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We study a symmetry property of momentum distribution functions in the steadystate of heat conduction. When the equation of motion is symmetric under changeof signs for all dynamical variables, the distribution function is alsosymmetric. This symmetry can be broken by introduction of an asymmetric term inthe interaction potential or the on-site potential, or employing the thermalwalls as heat reservoirs. We numerically find differences of behavior of themodels with and without the on-site potential.Comment: 13 pages. submitted to JPS

A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction