TY - JOUR

T1 - Derivation of Ohm's law in a deterministic mechanical model

AU - Chernov, N. I.

AU - Eyink, G. L.

AU - Lebowitz, J. L.

AU - Sinai, Ya G.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevLett.70.2209

DO - 10.1103/PhysRevLett.70.2209

M3 - Article

C2 - 10053503

AN - SCOPUS:0001688902

VL - 70

SP - 2209

EP - 2212

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 15

ER -