Fluctuation of the entropy production for the Lorentz gas under small external forces

Document Type

Article

Publication Date

2018

Abstract

In this paper we study the physical and statistical properties of the periodic Lorentz gas with finite horizon driven to a non-equilibrium steady state by the combination of non-conservative external forces and deterministic thermostats. A version of this model was introduced by Chernov, Eyink, Lebowitz, and Sinai and subsequently generalized by Chernov and the third author. Non-equilibrium steady states for these models are SRB measures and they are characterized by the positivity of the steady state entropy production rate. Our main result is to establish that the entropy production, in this context equal to the phase space contraction, satisfies the Gallavotti–Cohen fluctuation relation. The main tool needed in the proof is the family of anisotropic Banach spaces introduced by the first and third authors to study the ergodic and statistical properties of billiards using transfer operator techniques.

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Copyright Springer-Verlag GmbH Germany, part of Springer Nature 2018

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Publication Title

Communications in Mathematical Physics

Published Citation

Demers, M. F., Rey-Bellet, L., & Zhang, H. K. (2018). Fluctuation of the entropy production for the Lorentz gas under small external forces. Communications in Mathematical Physics, 363(2), 699-740. doi:10.1007/s00220-018-3228-3.

DOI

10.1007/s00220-018-3228-3

Peer Reviewed

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