Non-stochastic Langevin equation and the arrow of time

The behavior of a Brownian particle coupled to a linear harmonic chain is studied using a non-stochastic analysis. We show how a non-stochastic time correlation function of the fluctuating force reproduces the essential properties of the stochastic correlation function under not too restrictive conditions. The width of our correlation function is ω_m^-1 in time and, for time scales ≫ω_m^-1, behaves as a delta function. We discuss how irreversible-like behavior might occur in spite of the reversibility of our Langevin equation and how irreversibility depends upon a restricted narrow class of initial conditions. Our results thus help dispel the mystery of the "arrow of time".