Entropy Production, Fractals, and Relaxation to Equilibrium

T. Gilbert, J. R. Dorfman, and P. Gaspard
Phys. Rev. Lett. 85, 1606 – Published 21 August 2000
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Abstract

The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main ideas by using a simple multibaker model, with some nonequilibrium initial state, and we study its progress toward equilibrium. The central results are (i) the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space, (ii) the rate of entropy production is largely independent of the scale of resolution used in the partitions, and (iii) the rate of entropy production is in agreement with the predictions of nonequilibrium thermodynamics.

  • Received 7 March 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.1606

©2000 American Physical Society

Authors & Affiliations

T. Gilbert* and J. R. Dorfman

  • Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742

P. Gaspard

  • Center for Nonlinear Phenomena and Computer Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, Blvd du Triomphe, B-1050 Brussels, Belgium

  • *Current address: Laboratoire de Physique Théorique de la Matière Condensée, Université Paris VII, B.P. 7020, Place Jussieu, 75251 Paris cedex, France.

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Vol. 85, Iss. 8 — 21 August 2000

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