Continuous and discontinuous realizations of first-order phase transitions

Abstract: First-order phase transitions are commonly associated with a discontinuous behavior of some of the thermodynamic variables and the presence of a latent heat. In the present study it is shown that this is not necessarily the case. Using standard thermodynamics, the general characteristics of phase transitions are investigated, considering an arbitrary number of conserved particle species and coexisting phases, and an arbitrary set of state variables. It is found that there exist two different possible types of realizations of a phase transition. In the first type, one has the immediate replacement of a single phase with another one. As a consequence, some of the global extensive variables indeed behave discontinuously. In the second type, one has instead the gradual (dis-) appearance of a single phase over a range of the state variables. This leads to a continuous behavior of the (global) basic thermodynamic variables. Furthermore, in this case it is not possible to define a latent heat in a trivial manner. It is derived that the latter (former) case happens if the number of extensive state variables used is larger or equal (lower) than the number of coexisting phases. The choice of the state variables thus place a crucial role for the qualitative properties of the phase transition.