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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2006

Dynamics of a tracer granular particle as a non-equilibrium Markov process

Résumé

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend upon the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (pdf), the stationary velocity pdf of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient $\\alpha$. As soon as the velocity pdf of the gas departs from the Gaussian form, detailed balance is violated. This non-equilibrium state can be characterized in terms of a Lebowitz-Spohn action functional $W(\\tau)$ defined over trajectories of time duration $\\tau$. We discuss the properties of this functional and of a similar functional $\\bar{W}(\\tau)$ which differs from the first for a term which is non-extensive in time. On the one hand we show that in numerical experiments, i.e. at finite times $\\tau$, the two functionals have different fluctuations and $\\bar{W}$ always satisfies an Evans-Searles-like symmetry. On the other hand we cannot observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC) relation, which is expected for $W(\\tau)$ at very large times $\\tau$. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring $W(\\tau)$ and $\\bar{W}(\\tau)$ in experiments.

Dates et versions

hal-00018518 , version 1 (03-02-2006)

Identifiants

Citer

Andrea Puglisi, Paolo Visco, Emmanuel Trizac, Frederic van Wijland. Dynamics of a tracer granular particle as a non-equilibrium Markov process. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2006, 73 (2), pp.021301. ⟨10.1103/PhysRevE.73.021301⟩. ⟨hal-00018518⟩
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