Comparative Study on Several Criteria for Non-equilibrium Phase Separation

TL;DR

This paper compares various criteria for identifying the stages of non-equilibrium phase separation, highlighting the advantages of physical criteria over geometric ones in determining critical transition times.

Contribution

It systematically evaluates geometric and physical criteria for phase separation, emphasizing the effectiveness of non-equilibrium strength and entropy production rate as physical indicators.

Findings

Geometric criteria provide rough estimates for crossover times.

Physical criteria like non-equilibrium strength are more accurate and convenient.

Different criteria offer complementary perspectives on phase separation.

Abstract

Several different kinds of criteria for non-equilibrium phase separation to discriminate the two stages, the spinnodal decompostion (SD) and domain growth (DG), are compared and further investigated. The characteristic domain size and morphological function present two geometric criteria. Both of them can only provide rough estimations for the crossover from SD to DG. The reason for domain size is that the crossover in this description covers a process, instead of a specific time. The reason for the morphological function is that the result may rely on chosen threshold value. However, both the non-equilibrium strength and the entropy production rate are physical criteria and are more convenient to provide critical times. In fact, not only the non-equilibrium strength defined in the moment space opened by all the independent components of the used non-equilibrium quantities but also those defined in its subspaces can be used as criteria. Each of those criteria characterizes the phase separation process from its own perspective. Consequently, the obtained critical times may show slight differences. It should be pointed out that these slight differences are not contradictive, but consistent with each other and complementary in describing the complex phenomena.