Derivation of Ohm's law in a deterministic mechanical model

N. I. Chernov, G. L. Eyink, J. L. Lebowitz, Ya G. Sinai

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157 Scopus citations


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 languageEnglish (US)
Pages (from-to)2209-2212
Number of pages4
JournalPhysical review letters
Issue number15
StatePublished - 1993

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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