Abstract
In this chapter, we conjecture the “linear ansatz” equation of evolution of the order parameter, which is consistent with the laws of thermodynamics. We analyze solutions of this equation in different situations: close to the equilibrium state, far away from it, or when the evolution is taking place close to the spinodal point. Analyzing stability of homogeneous equilibrium states we find that the criteria of their dynamic and thermodynamic stability coincide. We also take a step beyond the linear ansatz and look at the order parameter evolution in systems with memory. One of the conclusions that we arrive at is that all of the above considered cases do not describe a phase transition completely because they cannot describe overcoming of a potential barrier by the system. Hence, other forces ought to be included into the complete theory.KeywordsLyapunov FunctionAmplification FactorSmall DisturbanceSpinodal PointFull MemoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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