Entropy production along a stochastic trajectory and an integral fluctuation theorem

For stochastic nonequilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and entropy production in the surrounding medium. The integrated sum of both Delta s(tot) is shown to obey a fluctuation theorem < exp[-Delta s(tot)]>=1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.