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Nonequilibrium entropy. Characterization of stationary states

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  • Pérez-Madrid, A.

Abstract

A generalization of the Gibbs entropy postulate is proposed based on the BBGKY [Born–Bogoliubov–Green–Kirkwood–Yvon] hierarchy as the nonequilibrium entropy for a system of N interacting particles. By using this entropy and the methods of nonequilibrium thermodynamics, a master equation for the evolution of the distribution vector is derived. In addition, after neglecting correlations in this master equation the Boltzmann equation is obtained. Moreover, our theory enables us to characterize the nonequilibrium stationary states as the states of constant entropy avoiding divergences in the entropy. Nonequilibrium Green–Kubo type relations are also derived.

Suggested Citation

  • Pérez-Madrid, A., 2007. "Nonequilibrium entropy. Characterization of stationary states," Energy, Elsevier, vol. 32(4), pages 301-305.
  • Handle: RePEc:eee:energy:v:32:y:2007:i:4:p:301-305
    DOI: 10.1016/j.energy.2006.06.015
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    References listed on IDEAS

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    1. Bedeaux, D. & Mazur, P., 2001. "Mesoscopic non-equilibrium thermodynamics for quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(1), pages 81-100.
    2. Pérez-Madrid, A. & Rubí, J.M. & Mazur, P., 1994. "Brownian motion in the presence of a temperature gradient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(3), pages 231-238.
    3. Mayorga, M. & Romero-Salazar, L. & Rubı́, J.M., 2002. "Stochastic model for the dynamics of interacting Brownian particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(3), pages 297-314.
    4. Mazur, P, 1999. "Mesoscopic nonequilibrium thermodynamics; irreversible processes and fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(3), pages 491-504.
    5. Ruelle, David, 1999. "Gaps and new ideas in our understanding of nonequilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 540-544.
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