Dynamics of Homogeneous Systems

Document Type

Book

Publication Date

1-1-2023

Abstract

In Chaps. 8 and 9, we concentrated on the states of thermodynamic equilibrium. However, an OP, as any hidden variable, characterizes a possibility for a system to occupy a nonequilibrium state. Thus, we now turn our attention to the situations when the system initially is not in one of the states of equilibrium and would like to know what happens to the system next. Specifically, we want to answer the following question: What is the equation that describes evolution of the OP in a nonequilibrium system? Experiments show that in all systems there is a tendency to evolve toward equilibrium states, which are determined by intrinsic properties of the system and not by the initial influences; see zeroth law in Sect. 1.1. In this chapter we conjecture the “linear-ansatz” equation of evolution of the order parameter, which is consistent with all the laws of thermodynamics; see Sect. 1.1. 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. We start with a homogeneous system and consider inhomogeneous systems in Chap. 11. 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 the situations considered in Chaps. 8 and 9 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. Regarding the beams and columns configuration of FTM in Fig. P.1, in this chapter we start building column 4.

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