Phase transition in the Jarzynski estimator of free energy differences.

The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems the directionality of time is poorly defined and the configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled.

Entropy, information, and the arrow of time.

We shall investigate the relationships between the thermodynamic entropy and information theory and the implications that can be drawn for the arrow of time. This demands a careful study of classical thermodynamics and a review of its fundamental concepts. The statistical mechanical properties of time-dependent systems will be carefully studied, and the point at which the arrow of time appears will be described.