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 Deltastot is shown to obey a fluctuation theorem <exp[-Deltastot]>=1 for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.

thermostat "fluctuation theorem"

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.

The Jarzynski equality (JE) and the undergirding Crooks fluctuation theorem (CFT) have generated intense interest recently among researchers in physical and biological sciences. It has been held that the CFT has wider applicability than the JE. This note shows that the two are equally applicable and that their applicability is possibly limited to near-equilibrium processes, where the linear fluctuation-dissipation theorem holds.