2012/08/25 by Phil Attard, Attard, Phil
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Solidification and crystal growth phenomena #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1208.5105
25 pages, 8 figures
arxiv created 2012/08/25 · openalex publication_date 2012/08/25 · arxiv updated 2012/08/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Spontaneous transitions between non-equilibrium patterns are characterised by hydrodynamic calculations of ideal straight roll steady state heat convection. The calculations are tested quantitatively against existing experimental data. It is shown that at a given Rayleigh number the final wave number depends upon whether the initial state was the conducting state, or, in the case of the cross roll transition, the wave number of the initial straight roll state. The final wave number does not correspond to the maximum or to the minimum heat flux (entropy production or dissipation), nor to the maximum sub-system entropy. In all cases the entropy of the total system increases monotonically during the spontaneous transition. It is concluded that there does not exist any single time thermodynamic property or variational principle for non-equilibrium systems. It is further concluded that the second entropy is the two time variational principle that determines the optimum non-equilibrium state or pattern.