The essence of phase transitions in condensed matter by an information theoretic approach

Abstract

Our information theoretic considerations suggest that the essence of phase transitions in condensed matter is the change in entropy as reflected in the change in the number of isomers between two phases. The explicit number of isomers as a function of size is computed using a graph theoretic approach that is compared to a direct count for smaller systems. This allows us to apply a common approach to both nanosystems and their macroscopic limit. The entropy increases very rapidly with size with the results that replacing the actual distribution over size by an average is not an accurate approximation. That the phase transition is a sharp function of the temperature is due to the high heat capacity of both the solid and liquid phases. The difference in entropy at the transition is related to the Trouton–Richards considerations. The finite width of the boundary between two phases of a finite system is related to the inherent uncertainty product that is derived from the maximum entropy formalism and that is a result of the fluctuations about equilibrium. As the system size increases, the boundary becomes sharper and one recovers the usual thermodynamic description.