Landau Theory of Dynamic Critical Phenomena in the Rayleigh-Benard System

TL;DR

This paper develops a Landau theory-based framework for understanding dynamic critical phenomena in the Rayleigh-Bénard system, extending thermodynamic concepts to rate thermodynamics near critical points.

Contribution

It introduces a rate thermodynamics approach using a potential called rate entropy, applying Landau theory to analyze critical behavior in the Rayleigh-Bénard system.

Findings

Formulation of rate thermodynamics for Rayleigh-Bénard convection

Application of Landau theory near critical points

Introduction of rate entropy as a potential

Abstract

Physics involving more details than hydrodynamics is needed to formulate rate thermodynamics of the Rayleigh-B\'{e}nard system. The Boussinesq vector field is approached in the space of mesoscopic vector fields similarly as equilibrium sates are approached in externally unforced systems in the space of mesoscopic state variables. The approach is driven by gradient of a potential (called a rate entropy). This potential then provides the rate thermodynamics in the same way as the entropy provides thermodynamics for externally unforced systems. By restricting the investigation to a small neighborhood of the critical point we can use the rate-thermodynamic version of the Landau theory.