Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature

Details Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature

2010-03-12

arxiv.org/abs/1003.2585v1

Phys. Rev. E 81, 061107 (2010)

Physics

Condensed Matter

Statistical Mechanics

15 pages, 7 figures

Scientific paper

10.1103/PhysRevE.81.061107

The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable-dependence of the fluctuation-dissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.

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