Entropy production in open volume-preserving systems |
| |
Authors: | Pierre Gaspard |
| |
Institution: | (1) Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Bruxelles, Belgium |
| |
Abstract: | 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. |
| |
Keywords: | Entropy production flux boundary conditions nonequilibrium steady state singular measure multibaker map Takagi function |
本文献已被 SpringerLink 等数据库收录! |
|