Nuclear first order phase transition associated with Helmholtz free energy of canonical ensemble

TL;DR

This paper investigates a nuclear first order phase transition in a simple statistical model within the canonical ensemble, revealing unique thermodynamic behavior distinct from the traditional liquid-gas transition.

Contribution

It demonstrates that the nuclear phase transition in this model is associated with the Helmholtz free energy and exhibits distinct discontinuities in thermodynamic derivatives, differing from the classical liquid-gas transition.

Findings

Helmholtz free energy predicts a nuclear first order phase transition.

Discontinuities in energy, pressure, and chemical potential at the transition point.

Thermodynamic potential is piecewise smooth with piecewise continuous derivatives.

Abstract

It was shown that in the canonical ensemble the simple exactly soluble statistical model of nuclei decay into nucleons, which is a limiting case of the statistical multifragmentation model, predicts the nuclear first order phase transition associated with the Helmholtz free energy different from the first order phase transition of the liquid-gas type associated with the Gibbs free energy. The main thermodynamic properties of this phase transition were explored on the basis of the method of the thermodynamic potential and its first and second derivatives in the thermodynamic limit. It was established that the thermodynamic potential $F$ is a piecewise smooth function and its first order partial derivatives with respect to variables of state are piecewise continuous functions. At the points of phase transition, the energy in the caloric curve is discontinuous at the constant temperature and fixed values of the specific volume, while the pressure and the chemical potential in the equations of state are discontinuous at the constant specific volume and fixed values of the temperature.