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From the adiabatic piston to macroscopic motion induced by fluctuations

Author

Listed:
  • Piasecki, J.
  • Gruber, Ch.

Abstract

The controversial problem of the evolution of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the mass of the fluid particles we obtain a rigorous explicit stationary non-equilibrium solution of the Boltzmann equation. It is shown that at equal pressures on both sides of the piston, the temperature difference induces a non-zero average velocity, oriented toward the region of higher temperature. It thus turns out that despite the absence of macroscopic forces the asymmetry of fluctuations results in a systematic macroscopic motion. This remarkable effect is analogous to the dynamics of stochastic ratchets, where fluctuations conspire with spatial anisotropy to generate directed motion. However, a different mechanism is involved here. The relevance of the discovered motion to the adiabatic piston problem is discussed.

Suggested Citation

  • Piasecki, J. & Gruber, Ch., 1999. "From the adiabatic piston to macroscopic motion induced by fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 463-472.
  • Handle: RePEc:eee:phsmap:v:265:y:1999:i:3:p:463-472
    DOI: 10.1016/S0378-4371(98)00553-6
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    Cited by:

    1. Gruber, Ch. & Piasecki, J., 1999. "Stationary motion of the adiabatic piston," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(3), pages 412-423.
    2. Gruber, Christian & Lesne, Annick, 2005. "Hamiltonian model of heat conductivity and Fourier law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 358-372.

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