Entropy production in open volume-preserving systems

Details Entropy production in open volume-preserving systems Entropy production in open volume-preserving systems

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jsp....88.1215g&link_type=abstract

Journal of Statistical Physics, Volume 88, Issue 5-6, pp. 1215-1240

Physics

30

Entropy Production, Flux Boundary Conditions, Nonequilibrium Steady State, Singular Measure, Multibaker Map, Takagi Function

Scientific paper

We describe a mechanism leading to positive entropy production in volume-preserving systems under nonequilibrium conditions. We consider volume-preserving systems sustaining a diffusion process like the multibaker map or the Lorentz gas. A continuous flux of particles is imposed across the system resulting in a steady gradient of concentration. In the limit where such flux boundary conditions are imposed at arbitrarily separated boundaries for a fixed gradient, the invariant measure becomes singular. For instance, in the multibaker map, the limit invariant measure has a cumulative function given in terms of the nondifferentiable Takagi function. Because of this singularity of the invariant measure, the entropy must be defined as a coarse-grained entropy instead of the fined-grained Gibbs entropy, which would require the existence of a regular measure with a density. The coarse-grained entropy production is then shown to be asymptotically positive and, moreover, given by the entropy production expected from irreversible thermodynamics.

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