Degenerate physical states are often associated with structural changes in systems. Physics uses the concept of degeneracy in the modeling of the dynamics of state changes such as solid/liquid/gas.
In a two-state model, say, liquid/solid, degenerate states are favorable statistical states for the constituents of the system to adopt. These are offset by an energetically favoured state that constituents will tend to be in, say, the case of a solid state. This bias, generated by the energetically favoured state, will hold the system in this most probable state unless some condition, such as the energy available to the system, is modified. An example is water molecules that tend to stay in a crystalline formation (ice) in a sufficiently cold environment. As more energy is introduced in the system, such as a heat increases in the environment, a global shift in the system is more likely to occur. Interestingly enough the liquid/solid transition takes place suddenly at a critical temperature; an equilibrium system 4.3 is solid slightly below Tc€ =0c€ in the case of H2€0, and liquid slightly above. Liquifaction or crystallization occurs suddenly.
This kind of radical shift in the state of a related system variable is referred to as a first-order phase transition.
We think that a model capable of first order phase transition can be constructed using lexicality and functionality as states.
As we have discussed, lexical vocabulary, defined as more efficient requires little energy to use. In chapter three we argued that functionalized vocabulary is less efficient; that is, it requires more energy to use but does more work and as such, can propagate further. Lexical vocabulary provides a bias in the system as it represents the lower energy state. In order for the system to change structurally, energy must be made available to the system. In our language model, it is the effort involved in linguistic transactions that increases or decreases in a population of language users. An increase in effort has for effect an increase in the level of linguistic activity that will favor the propagation of vocables. We imagine that constraints such as a growing population or an increase in the sophistication of the coordination of human activity are responsible for an increase in linguistic activity. The natural tendency for lexical vocabulary to remain lexical, because its ease of use is greater, and the tendency for vocables to attenuate, increasing its portability but diminishing its ease of use, generates a tension in the dynamics of the system. If enough linguistic activity occur in the population of language users, this tension will influence how structural changes happen. Given these conditions, a first order phase transition is a likely eventuality. This means that a lexical vocable, or more likely an attenuated vocable, can suddenly acquire functionalized instances in a very short timespan. This is a very particular instance of what may happen in the dynamics of language, but we assume that changes in the structure of vocables can occur in several different ways. We can also imagine changes occurring in a more progressive way.
There are at least two kinds of phase transitions: first order and second order. A second order phase transition is typified by a gradual change in structure or order. We will give an account of both phase transitions because their descriptions are dependent on each other, also, both accounts are relevant for a physical description of the behavior in the structural change of vocables.