Nonequilibrium Phase Transitions in Frozen Grounds

Abstract

At first, we discuss what is meant by equilibrium phase transition and nonequilibrium one. For equilibrium phase transition the concentration of an unfrozen water W coincides with Heaviside’s function W(x,t) = H(u(x,t)), here u(x,t) is the temperature,

$$H\left( u \right) = \left\{ {\begin{array}{*{20}{c}} {1, u > 0,} \hfill \\ { \in \left[ {0,1} \right], u = 0,} \hfill \\ {0, u < 0.} \hfill \\ \end{array} } \right. $$

u= 0 is the melting temperature. This means that under change of temperature u the concentration of water W takes instantaneously a new value corresponding to the new temperature. Meanwhile in real processes some finite time is required for achieving equilibrium between ice and an unfrozen water in the ground.