Thermodynamics for Non-equilibrium Pattern Formation
Abstract
The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is derived. The Navier-Stokes equations in Boussinesq approximation for straight roll convection are solved by a Fourier expansion technique. Results for the velocity amplitude are in good agreement with previous computations and experimental measurements. For the spontaneous transitions between straight roll states reported in the literature, it is shown that the measured change in convective pattern wave length corresponds to an increase in the entropy. This paper has been superseded by arXiv:1208.5105v1.
Cite
@article{arxiv.1102.2257,
title = {Thermodynamics for Non-equilibrium Pattern Formation},
author = {Phil Attard},
journal= {arXiv preprint arXiv:1102.2257},
year = {2012}
}
Comments
This paper is withdrawn due to a units conversion error that magnified the gravitational contribution to the entropy. The paper has been superseded by arXiv:1208.5105v1