Time evolution approach to steady state

Abstract

We apply a time evolution approach to the statistical mechanics of one and two dimensional systems to study the evolution toward steady state. We have used the Feynman definition of an inverse operator to show that in one and two dimensions, there is an approach to steady state of hydrodynamic variables such as field velocities and pressure. Illustrative examples in 1D are shown to display steady state variables. Keywords: Time evolution equations, Hydrodynamic variables, Ergodic behavior, Navier–Stokes equation, Recurrence, Boltzmann equation