### Abstract

We study the Lorentz gas in small external electric and magnetic fields, with the particle kinetic energy held fixed by a Gaussian ''thermostat.'' Starting from any smooth initial density, a unique stationary, ergodic measure is approached for times t→. The steady-state electric current J(B,E) is given by a Kawasaki formula and the entropy production JE/T, with T the ''temperature,'' is equal to both the asymptotic decay rate of the Gibbs entropy and minus the sum of the Lyapunov exponents. The Einstein and Kubo formulas hold, i.e., J(B,E)=σ(B)E + higher order terms, with the diffusion matrix D(B) at E=0 given by kBT times the symmetric part σ(B) of the conductivity matrix.

Original language | English (US) |
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Pages (from-to) | 2209-2212 |

Number of pages | 4 |

Journal | Physical review letters |

Volume | 70 |

Issue number | 15 |

DOIs | |

State | Published - Jan 1 1993 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Physical review letters*,

*70*(15), 2209-2212. https://doi.org/10.1103/PhysRevLett.70.2209