1993
DOI: 10.1103/physrevlett.70.2209
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Derivation of Ohm’s law in a deterministic mechanical model

Abstract: We study the Lorentz gas in small external electric and magnetic fields, E and B, with the particle kinetic energy held fixed by a Gaussian "thermostat" (a modification of a model of Moran and Hoover.) Here we prove rigorously that : (1) Starting from any smooth initial density, a unique stationary, ergodic measure (whose support is fractal) is approached for times t → ∞. (2) The steady-state electric current, J(B, E), is given by a Kawasaki formula and the entropy production J • E/T, with T the "temperature,"… Show more

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Cited by 174 publications
(188 citation statements)
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References 17 publications
(23 reference statements)
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“…Relations between the Lyapunov spectrum of the microscopic dynamics and macroscopic properties such as viscosity and heat conductivity have been established within the last years, most detailed for the Lorentz gas [16,17,18,19,20,21,22]. The severity and importance of these relations become apparent from the fact they have to bridge the gap between microscopic reversibility and macroscopic irreversibility challenging physicists since Ludwig Boltzmann.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…Relations between the Lyapunov spectrum of the microscopic dynamics and macroscopic properties such as viscosity and heat conductivity have been established within the last years, most detailed for the Lorentz gas [16,17,18,19,20,21,22]. The severity and importance of these relations become apparent from the fact they have to bridge the gap between microscopic reversibility and macroscopic irreversibility challenging physicists since Ludwig Boltzmann.…”
Section: Discussionmentioning
confidence: 99%
“…Thirdly, when tiny deviations of initial conditions that were not observable in the beginning are enlarged by the evolution, this can be interpreted as the production of information about the initial conditions. Finally, the KSE is known to be related to macroscopic properties such as transport coefficients [16,17,18,19,20,21,22].…”
Section: Introductionmentioning
confidence: 99%
“…• While it was emphasized that the extensivity of ∆D is not compatible with local equilibrium so that it is questionable [12]. As was mentioned above, violations of local equilibrium appear in the same manner as dimensional loss.…”
Section: Non-equilibrium Equation Of Statementioning
confidence: 99%
“…These characteristic features of thermostated many-particle systems have been recovered for specific one-particle systems, the Gaussian thermostated periodic Lorentz gas [11,15,18,19,[21][22][23][24] and the Nosé-Hoover thermostated periodic Lorentz gas [25]. The periodic Lorentz gas consists of a particle that moves through a triangular lattice of hard disks and is elastically reflected at each disk collision.…”
Section: Introductionmentioning
confidence: 99%
“…At the heart of such relations there is an identity between phase space volume contraction and thermodynamic entropy production. On the basis of this identity the Lyapunov exponents could be related to the transport coefficients of a system, which has been formulated as the Lyapunov sum rule [11,[17][18][19][20][21].…”
Section: Introductionmentioning
confidence: 99%