I am not sure what do you mean by including entropic effect, you can calculate the entropy and other thermal properties using quasi-harmonic approximation (QHA) in quantum espresso or vibrational properties in other softwares.

or maybe, if you run a molecular dynamics and graphic the change in the energy. You could put your entropy in function of the total energy of the system with respect to time (compute cycles in femtoseconds).

Hi Alec, You mentioned that entropy can be calculated using  molecular dynamics. But can you briefly explain me how entropy can be calculated using md?

The so-called "entropy " doesn't exist at all.

During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.

The so-called entropy was such a concept that was derived by mistake in history.

It is well known that calculus has a definition,

any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.

Based on the definition of calculus, we know:

to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.

As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,

∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.

1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.

2) On the other hand, In fact, Q=f(P, V, T), then

∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).

We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.

that is, the so-called "entropy " doesn't exist at all.

Dear Shufeng Zhang

dQ/T is the change of entropy not the absolute entropy. We can regard entropy as the measure of information. For example for ICE cube the molecule is in a fixed position on the other hand in water the molecules wander around randomly. We need more information to describe the position of molecules in water as a result the entropy of water is higher than the ice cube.

Now if we want to calculate how much entropy is increased for phase transition of ice to liquid phases we can use the equation dQ/T,