Cugliandolo wrote a survey last year of recent work involving the effective temperature. This is a macroscopic quantity that characterizes a system driven out of equilibrium. The review states that the effective temperature was initially used as an intuitive description of glassy and slowly relaxing systems, but only recently have theoreticians placed it on firmer ground by linking it to the fluctuation-dissipation theorem (FDT).
In practice, the effective temperature is the negative inverse slope of a system's dc susceptibility (a.k.a. its time-integrated impulse response) vs. the time-correlation function of some observable (a.k.a. the description of its thermal fluctuations). Importantly, a departure from the straight line joining the points (1,0) and (0, 1/temperature) on a properly normalized plot may signify a system that is not at equilibrium with its bath. In the paper, Cugliandolo assumes a canonical ensemble, or a system coupled to an equilibriated thermal bath. Also, because it is based on the FDT, this treatment is only valid for extremely small perturbations to the system such that an impulse response is an appropriate description.
Most recent work has been focused on determining whether the effective temperature meets our intuitive requirements for a temperature, like being measurable by a thermometer, and whether it is an appropriate thermodynamic description, i.e. it is a single number that summarizes the state of a large ensemble of random system parts. It seems that very slow relaxations, either forced or natural, must be present for this quantity to be useful.
A "lab notebook" about my life in science, programming, and philosophy.
