I think it is possible as long as the system is locally in equilibrium (metastable). I think then the corresponding functions can be well defined.

Dear Andreas,

Thanks for your answer.

'The system is locally in equilibrium (metastable)' may mean that the system can be divided into subsystems and each subsystem is in a metastable state uniformly?.

Then, the energy of the whole system should be higher than that of the Gibbs energy in equilibrium ?

Dear Changming Fang,

The Gibbs energy is not only a term for equilibrated system.

It is easier to think about it by making a parallel with other forms of energy, as in https://doi.org/10.1007/978-1-4615-1237-0 or https://doi.org/10.1557/mrs.2019.162.

So, let’s consider a dam with a water reservoir on one side and an empty lake on the other. At the time you open the dam, you are out of equilibrium, but you can still compute the gravitational energy of your system (as a whole, but also of both subsystems). Then, there will be an exchange of mass of water from high heights to low heights until the gravitational energy of the system is minimized at equilibrium.

If we consider a gradient of composition in a miscible liquid, there will be an exchange of moles from high chemical potentials to low chemical potentials until the Gibbs energy of the system is minimized at equilibrium. But you can compute the Gibbs energy anytime (if you know the Gibbs energy of the phases involved), which can give a measure of the driving force for the change to occur.

Best regards,

Dear Guillaume,

Thanks for your answer.

I agree with you that Gibbs energy can be used to measure the potential difference between different Equilibrated systems.

That is how we use this term (difference of Gibbs energy) to measure chemical reactions. However, if I am not wrong, we assumed that each of the system is at equilibrium.

What I want to understand is the question: e.g. in a solidification process, the system is in fact in non-equilibrium and people also used Gibbs energy, or related interface energy between liquid and solid to discuss such processes.

Probably, there are some underlining assumptions behind.

Dear Changming,

Sorry I misunderstood the question. Maybe we think about something different, or at a different scale, when we speak about equilibrium. I will just add this in case it's useful: we can reasonably extrapolate the Gibbs energy of, e.g., liquid Sn, in the undercooled region where it’s not at thermodynamic equilibrium.

Dear Guillaume,

Thanks for your comments. I agree with you that there are different understanding about equilibrium of a system. To explore the systems deviating from equilibrium, some assumptions have to be made. Supercooling or glass is indeed not in its equilibrium but it might be a metastable case as mentioned by Andreas. Such situation can be in principles described by thermodynamics. The example you raised early can be used to describe them.

Dear Dr. Rana Hamza Shakil,

Thank you very much for sharing the information.