Gibbs Free Energy: Equilibrium and Dynamics

Equilibrium thermodynamics of Gibbs is sometimes referred to as “thermostatics”. This title reflects the essence of the formulated Gibbs thermodynamics, which establishes potentials only for the initial and final states of the system. Gibbs thermodynamics does not consider the evolution itself and the dynamics of the transition between these states. Therefore, a “thermostatic” description was further extended by taking the evolutionary transfer equations into account and with the description of the dynamics of the transition from one state of the system to another. Such a formalism is usually associated with the formulation of the thermodynamics of irreversible processesThermodynamicsof irreversible processes of Onsager and PrigogineThermodynamicsof Onsager and Prigogine. Based on the hypothesis of local equilibrium, this irreversible thermodynamics became the basis for formulating the entropy or free energyEnergyfree functionals of the phase field models. Therefore, to describe the basic states and classical dynamics, this chapter considers (a) the formulation of the Gibbs–Thomson condition based on classical Gibbs thermodynamics, and (b) the velocity-dependent Gibbs–Thomson condition compatible with the classical phase field model based on the local equilibrium formulation of Onsager-Prigogine thermodynamics.