Thermodynamics for Non-equilibrium Pattern Formation

TL;DR

This paper applies the second entropy theory to non-equilibrium thermodynamics, deriving formulas and solving equations to explain pattern formation and transitions in convective heat flow, linking entropy changes to pattern dynamics.

Contribution

It introduces a maximum entropy principle for non-equilibrium pattern formation and provides analytical solutions for convective flow patterns using the second entropy theory.

Findings

Velocity amplitude results agree with previous data

Entropy increases during pattern transitions

Derived a formula for total entropy of convective heat flow

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 This paper has been superseded by arXiv:1208.5105v1.