  A macroscopically uniform model of a two-dimensional electron system is
proposed to study nonequilibrium properties of electrical conduction. By
molecular dynamics simulation, the steady state distribution function $P_y$ of
electron velocity in a direction perpendicular to an external driving force is
calculated. An explicit form of $P_y$ is determined within the accuracy of the
numerical simulation, which fits the numerical data well even in the regime
where a local equilibrium description is not valid. Although the entire
structure of $P_y$ is different from that of a local equilibrium distribution
function, the asymptotic structure of the tails of $P_y$ in the limit of large
absolute values of the velocity is identical to that of a Maxwell distribution
function with a temperature which is different from that in the equilibrium
state and the kinetic temperature in the steady state.
