Out of equilibrium thermodynamics study often changes in a structure with a long time scale. Could first order transitions give informations to out of equilibrium evolving structures? I mean: the time scale in a first order transition tends to zero (for example liquid solid transition), but the involved systems are often more simple. I would suggest scientists to study first order transitions as if they were out of equilibrium (during the duration of the transition).
That's the reason why Becker-Döring cluster theory and its modifications (coagulation-fragmentation equations) is still quite popular amongst mathematicians and physicists. One investigates e.g. the first-order phase transition "gas -> liquid" via the formation of larger and larger clusters, formed out of a monomer bath (i.e. the gaseous phase). Here a cluster consists of several monomers sticking together. Once a critical clustersize is exceeded one identifies these "large" clusters with the occurance of droplets (i.e. the liquid phase).
The stochastic processes of cluster formation are usually described by master equations. For Markovian stochastic processes these master equations are represented by infinite systems of ordinary differential equations of 1st order in the time parameter t. And as you observed correctly, under certain conditions one recovers a time scale tending to zero, i.e. metastable states. Furthermore, as you also mentioned, the physical systems are far from equilibrium. Hence Onsager's reciprocity relations approach is not applicable. Oliver Penrose, a former post-doc of Lars Onsager, has dedicated quite some time researching the issues you mentioned in the 70s, 80s and 90s, also Kurt Binder, Joel Lebowitz and Enzo Olivieri to name but a few pioneers.
A drawback of this mathematical picture, however, is the need of a micro-physical theory for the transition rates. If one really had a serious theory of the transition rates for water and the "liquid -> solid" phase transition ("freezing"), say, then one could investigate a possible theoretical explanation for the Mpemba effect.
Markus, thanks for your interesting post. But I do not think that water is 'simple' to study. I would suggest other liquid-solid transitions. Maybe the roots of a microphysical theory would be in quantum mechanics? that 's just a suggestion...I hardly believe that a markovian approach would be the solution, especially for water
(or maybe yes? -the characteristic length for hot water is maybe larger than cold water and the 'characteristic length' -i.e. crystalline dimension- of ice is closer to that of hot water- Mpemba effect??? but why???)
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Thermodynamics