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Nonequilibrium fluctuations in a driven stochastic Lorentz gas

G. Gradenigo, A. Puglisi, and A. Sarracino

U. Marini Bettolo Marconi

CNR-ISC and Dipartimento di Fisica, Università Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy

Scuola di Scienze e Tecnologie, Università di Camerino, 62032 Camerino, Italy

Phys. Rev. E 85, 031112 – Published 9 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.031112

Abstract

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field $E$ and collides, elastically or inelastically, with a bath of particles at temperature $T$ . We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production $Δ s_{tot}$ . One is the entropy production of the medium $Δ s_{m}$ , which is equal to the energy exchanged with the scatterers, divided by a parameter $θ$ , coinciding with the particle temperature at $E = 0$ . The other is the work $W$ done by the external field, again rescaled by $θ$ . At small $E$ , a good collapse of the two distributions is found: in this case, the two quantities also verify the fluctuation relation (FR), indicating that both are good approximations of $Δ s_{tot}$ . Differently, for large values of $E$ , the fluctuations of $W$ violate the FR, while $Δ s_{m}$ still verifies it.

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