Thermodynamics of Third Order Phase Transition: A Solution to the Euler-Lagrange Equations

TL;DR

This paper investigates the thermodynamics of third order phase transitions by deriving and solving Euler-Lagrange equations for the order parameter and vector potential, providing new analytical solutions in this domain.

Contribution

It introduces a novel analytical approach to third order phase transitions through the derivation and solution of Euler-Lagrange equations for relevant thermodynamic variables.

Findings

Derived Euler-Lagrange equations for third order phase transitions

Obtained analytical solutions for order parameter and vector potential

Enhanced understanding of thermodynamic behavior in higher-order phase transitions

Abstract

The thermodynamics expected of systems undergoing third order phase transition has been investigated by identifying the orders through the analytic continuation of the functional of the free energy, using Ehrenfest thermodynamic theory. We developed the Euler - Lagrange equations for the order parameter and the vector potential and solved them for the first time using well - known mathematical formulations.