Initial conditions in non-equilibrium statistical mechanics

Using an iterative projection technique method, a time-evolution equation is derived for the single-particle distribution function. An initial condition with built-in temperature and density discontinuities is used. It is shown that four soliton pairs traveling from the discontinuities may be generated. For the case of a density discontinuity alone, the classical shock tube result is recovered. It is also shown that with a temperature discontinuity, such as may be found in two metals which are brought together, it is possible to generate charged solitary pulses, in addition to the expected flow of electrons across the boundary.